| { | |
| "paper_id": "T78-1028", | |
| "header": { | |
| "generated_with": "S2ORC 1.0.0", | |
| "date_generated": "2023-01-19T07:51:42.645345Z" | |
| }, | |
| "title": "Fragments of a Theory of Human Plausible Reasoning", | |
| "authors": [ | |
| { | |
| "first": "Allan", | |
| "middle": [ | |
| "Collins" | |
| ], | |
| "last": "Bolt Beranek", | |
| "suffix": "", | |
| "affiliation": {}, | |
| "email": "" | |
| } | |
| ], | |
| "year": "", | |
| "venue": null, | |
| "identifiers": {}, | |
| "abstract": "", | |
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| "paper_id": "T78-1028", | |
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| "abstract": [], | |
| "body_text": [ | |
| { | |
| "text": "The paper outlines a computational theory of human plausible reasoning constructed from analysis of people's answers to everyday questions.", | |
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| "section": "", | |
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| "text": "Like logic, the theory is expressed in a content-independent formalism. Unlike logic, the theory specifies how different information in memory affects the certainty of the conclusions drawn. The theory consists of a dimensionalized space of different inference types and their certainty conditions, including a variety of meta-inference types where the inference depends on the person's knowledge about his own knowledge.", | |
| "cite_spans": [], | |
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| "text": "The protocols from people's answers to questions are analyzed in terms of the different inference types.", | |
| "cite_spans": [], | |
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| "text": "The paper also discusses how memory is structured in multiple ways to support the different inference types, and how the information found in memory determines which inference types are triggered.", | |
| "cite_spans": [], | |
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| "text": "The goal of this paper is to briefly describe a theory of human plausible reasoning I am currently developing (Collins, 1978) . The theory is a procedural theory and hence one which can be implemented in a computer, as parts of it have been in the SCHOLAR and MAP-SCHOLAR systems (Carbonell & Collins, 1973; Collins & Warnock, 1974; Collins, Warnock, Aiello & Miller, 1975) .", | |
| "cite_spans": [ | |
| { | |
| "start": 110, | |
| "end": 125, | |
| "text": "(Collins, 1978)", | |
| "ref_id": "BIBREF1" | |
| }, | |
| { | |
| "start": 280, | |
| "end": 307, | |
| "text": "(Carbonell & Collins, 1973;", | |
| "ref_id": "BIBREF2" | |
| }, | |
| { | |
| "start": 308, | |
| "end": 332, | |
| "text": "Collins & Warnock, 1974;", | |
| "ref_id": "BIBREF3" | |
| }, | |
| { | |
| "start": 333, | |
| "end": 373, | |
| "text": "Collins, Warnock, Aiello & Miller, 1975)", | |
| "ref_id": "BIBREF5" | |
| } | |
| ], | |
| "ref_spans": [], | |
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| "section": "INTRODUCTION", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The theory is expressed in the production-rule formalism of Newell (1973) .", | |
| "cite_spans": [ | |
| { | |
| "start": 60, | |
| "end": 73, | |
| "text": "Newell (1973)", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "INTRODUCTION", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Unlike logic, the theory specifies how different configurations of information affect the certainty of the conclusions drawn.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "INTRODUCTION", | |
| "sec_num": null | |
| }, | |
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| "text": "These certainty conditions are in fact the major contribution of the theory.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "INTRODUCTION", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "To construct a theory of human plausible reasoning, I collected about 60 answers to everyday questions from 4 different subjects. The questions ranged from whether there are black princess phones to when the respondent first drank beer.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
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| "section": "Methodology of Constructing the Theory", | |
| "sec_num": null | |
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| "text": "The analysis of the protocols attempts to account for the reasoning and the conclusions drawn in the protocols in terms of: I) a taxonomy of plausible inference types, 2) a taxonomy of default assumptions, and 3) what the subject must have known a priori.", | |
| "cite_spans": [], | |
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| "section": "Methodology of Constructing the Theory", | |
| "sec_num": null | |
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| "text": "As will be evident, this is an inferential analysis. I am trying to construct a deep structure theory from the surface structure traces of the reasoning process.", | |
| "cite_spans": [], | |
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| "section": "Methodology of Constructing the Theory", | |
| "sec_num": null | |
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| "text": "The protocols have the following characteristics. I) There are usually several different inference types used to answer any question.", | |
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| "text": "2) The same inference types recur in many different answers.", | |
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| "section": "Methodology of Constructing the Theory", | |
| "sec_num": null | |
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| "text": "3) People weigh all the evidence they find that bears on a question. 4) People are more or less certain depending on the certainty of the information, the certainty of the inferences, and on whether different inferences lead to the same or opposite conclusions.", | |
| "cite_spans": [], | |
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| "text": "can illustrate some of these characteristics of the protocols as well as several of the inference types in the theory with a protocol taken from a tutorial session on South American geography (Carbonell & Collins, 1973 ):", | |
| "cite_spans": [ | |
| { | |
| "start": 192, | |
| "end": 218, | |
| "text": "(Carbonell & Collins, 1973", | |
| "ref_id": "BIBREF2" | |
| } | |
| ], | |
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| "section": "I", | |
| "sec_num": null | |
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| "text": "(T) There is some jungle in here (points to Venezuela) but this breaks into a savanna around the Orinoco (points to the Llanos in Venezuela and Colombia).", | |
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| "section": "I", | |
| "sec_num": null | |
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| "text": "(S) Oh right, that is where they grow the coffee up there? (T) I don't think that the savanna is used for growing coffee.", | |
| "cite_spans": [], | |
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| "section": "I", | |
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| "text": "The trouble is the savanna has a rainy season and you can't count on rain in general. But I don't know.", | |
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| "section": "I", | |
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| "text": "This area around Sao Paulo (in Brazil) is coffee region, and it is sort of getting into the savanna region there.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 27, | |
| "end": 39, | |
| "text": "(in Brazil)", | |
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| "text": "In the protocol the tutor went through the following reasoning on the question of whether coffee is grown in the Llanos. Initially, the tutor made a hedged \"no\" response for two reasons. First, the tutor did not have stored that the Llanos was used for growing coffee. Second, the tutor knew that coffee growing depends on a number of factors (e.g., rainfall, temperature, soil, and terrain), and that savannas do not have the correct value for growing coffee on at least one of those factors (i.e., reliable rainfall).", | |
| "cite_spans": [], | |
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| "text": "However, the tutor later hedged his initial negative response, because he found some positive evidence.", | |
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| "text": "In particular, he thought the Brazilian savanna might overlap the coffee growing region in Brazil around Sao Paulo and that the Brazilian savanna might produce coffee. Thus by analogy the Llanos might also produce coffee.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
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| "section": "I", | |
| "sec_num": null | |
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| "text": "Hence, the tutor ended up saying \"I don't know.\"", | |
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| "text": "The answer exhibits a number of the important aspects of the protocols. In general, a number of inferences are used to derive an answer.", | |
| "cite_spans": [], | |
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| "section": "I", | |
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| "text": "Some of these are inference chains where the premise of one inference depends on the conclusion of another inference.", | |
| "cite_spans": [], | |
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| "section": "I", | |
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| "text": "In other cases the inferences are independent sources of evidence. When there are different sources of evidence, the subject weighs them together to determine his conclusion.", | |
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| "text": "It is also apparent in this protocol how different pieces of information are found over time. What appears to happen is that the subject launches a search for relevant information (Collins & Loftus, 1975) . As relevant pieces of information are found (or are found to be missing), they trigger particular inferences.", | |
| "cite_spans": [ | |
| { | |
| "start": 180, | |
| "end": 204, | |
| "text": "(Collins & Loftus, 1975)", | |
| "ref_id": "BIBREF4" | |
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| "text": "The type of inferenoe applied is determined by the relation between the information found and the question asked. For example, if the subject knew that savannas are in general good for growing coffee, that would trigger a deduction. If the subject knew of one savanna somewhere that produced coffee, that would trigger an analogy. The search for information is such that the most relevant information is found first. In the protocol, the more relevant information about the unreliable rainfall in savannas was found before the more far fetched information about the coffee growing region in Brazil and its relation to the Brazilian savanna. Thus, information seems to be found at different times by an autonomous search process, and the particular information found determines inferences that are triggered.", | |
| "cite_spans": [], | |
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| "text": "The theory specifies a large number of different inference types, together with the conditions that affect the certainty of each inference type.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
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| "section": "THE THEORY", | |
| "sec_num": null | |
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| { | |
| "text": "In the theory the different types of inference are arrayed in a five dimensional space. (Brown, 1977) , such as lack-of-knowledge and confusability inferences.", | |
| "cite_spans": [ | |
| { | |
| "start": 88, | |
| "end": 101, | |
| "text": "(Brown, 1977)", | |
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| "text": "I refer to these latter as meta-inferenees.", | |
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| "text": "They are ubiquitous in the protocols, and yet they fall outside the scope of most theories of logic. The other four dimensions refer to the space of inferences but may also partially apply to the space of meta-inferences.", | |
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| "text": "(2) Functional vs Set Inferences For each type of inference, there is a functional variation and a set variation.", | |
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| "text": "The set variation involves mapping the property of one set (which may be a single-member set or instance) onto another set.", | |
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| "text": "The functional variation has an additional premise that the property to be mapped (the dependent variable) depends on other properties, (the independent variables).", | |
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| "text": "The mapping of the property from one set to another makes use of this functional dependency.", | |
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| "text": "The set variation, in fact, is a degenerate form of the functional variation, which is used when people have little or no knowledge of the functional dependencies involved.", | |
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| "text": "People's knowledge about functional dependencies consists of a kind of directional correlation.", | |
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| "text": "A judgment about whether a place can grow coffee might depend on factors that are causal precursors for coffee growing (e.g., temperature), correlated factors (e.g., other types of vegetation), or factors causally subsequent to coffee growing (e.g., export trade).", | |
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| "text": "For example, one might decide a place does not produce coffee, because it produces apples which seem incompatible with coffee, or because there is little export trade from the region.", | |
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| "text": "The directional nature of the correlation shows up in the last example.", | |
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| "text": "A region easily could have export trade without producing coffee, but it would be unlikely that a region would produce coffee without having export trade.", | |
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| { | |
| "text": "( (Quillian, 1968; Schank, 1972) . Spatial inferences are based on information (or images) derived from a spatial structure (Collins & Warnock, 1975; Kosslyn & Schwartz, 1977) .", | |
| "cite_spans": [ | |
| { | |
| "start": 2, | |
| "end": 18, | |
| "text": "(Quillian, 1968;", | |
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| "text": "(Collins & Warnock, 1975;", | |
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| "text": "Kosslyn & Schwartz, 1977)", | |
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| "text": "Temporal inferences are based on information derived from an event (or episodic) structure (Tulving, 1972 (Quillian, 1968; Schank, 1972) . The nodes in the network are schemas, which are the kind of structured objects implied by the notion of frames (Minsky, 1975) or scripts (Schank & Abelson, 1977) .", | |
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| "end": 105, | |
| "text": "(Tulving, 1972", | |
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| "start": 106, | |
| "end": 122, | |
| "text": "(Quillian, 1968;", | |
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| "text": "(Schank & Abelson, 1977)", | |
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| "text": "The links between nodes represent different relations between the concepts.", | |
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| "text": "The correlate of this kind of semantic structure in Winograd's SHRDLU (1972) was the cross-referenced information structure constructed by MICROPLANNER.", | |
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| "start": 52, | |
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| "text": "Winograd's SHRDLU (1972)", | |
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| "text": "Information. I assume spatial information about concepts, such as the size, shape, color, or location of objects and places, is represented in a spatial structure, apart from but connected to the semantic structure (Collins & Warnock, 1974) . The correlate of such a spatial representation in Winograd's SHRDLU (1972) was the Cartesian representation of the blocks on the table top.", | |
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| { | |
| "start": 215, | |
| "end": 240, | |
| "text": "(Collins & Warnock, 1974)", | |
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| "start": 293, | |
| "end": 317, | |
| "text": "Winograd's SHRDLU (1972)", | |
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| "section": "Spatial", | |
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| "text": "information. Similarly event information is assumed to be stored in a form that preserves its temporal, causal, and goal structure.", | |
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| "section": "Event", | |
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| "text": "This requires a hierarchical structure of events and subevents nested according to the goals and subgoals of the actors involved in the events (Brown, Collins, & Harris, 1978) .", | |
| "cite_spans": [ | |
| { | |
| "start": 143, | |
| "end": 175, | |
| "text": "(Brown, Collins, & Harris, 1978)", | |
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| "text": "Such an event memory was constructed by Winograd's SHRDLU (1972) to record the movements of blocks and the goals they accomplished, in order to answer \"why\" and \"how\" questions about events in the Blocks World.", | |
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| "start": 40, | |
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| "text": "Retrieval. I assume there are autonomous search processes that find relevant information with respect to any query (Collins & Loftus, 1975) . The search process has access to semantic, spatial and temporal information in parallel, and whenever relevant information of any kind is found, it triggers an inference (Collins & Quillian, 1972; Kosslyn, Murphy, Bemesderfer & Feinstein, 1977.) The information found by the search processes determines what inference patterns are applied.", | |
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| { | |
| "start": 115, | |
| "end": 139, | |
| "text": "(Collins & Loftus, 1975)", | |
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| { | |
| "start": 312, | |
| "end": 338, | |
| "text": "(Collins & Quillian, 1972;", | |
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| { | |
| "start": 339, | |
| "end": 387, | |
| "text": "Kosslyn, Murphy, Bemesderfer & Feinstein, 1977.)", | |
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| { | |
| "text": "Processes. I assume there are decision processes for determining whether any two concepts can be identified as the same. The semantic matching process could be that proposed by Collins & Loftus (1975) or by Smith, Shoben & Rips (1974) . The spatial matching process compares places or objects to decide their spatial relation.", | |
| "cite_spans": [ | |
| { | |
| "start": 177, | |
| "end": 200, | |
| "text": "Collins & Loftus (1975)", | |
| "ref_id": "BIBREF4" | |
| }, | |
| { | |
| "start": 207, | |
| "end": 234, | |
| "text": "Smith, Shoben & Rips (1974)", | |
| "ref_id": "BIBREF12" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Matching", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Similarly, there must be a temporal matching process that determines the relation between two events.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Matching", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "and CertaintE. I assume that for each concept and relation a person has a notion of its relative importance (i.e. its criteriality), and his degree of certainty about its truth. In a computer, these could be stored as tags on the concepts and relations (Carbonell & Collins, 1973) .", | |
| "cite_spans": [ | |
| { | |
| "start": 253, | |
| "end": 280, | |
| "text": "(Carbonell & Collins, 1973)", | |
| "ref_id": "BIBREF2" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Importance", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "it is impossible to present the entire theory here, I will give the formulations for three types of inference and show three protocols which illustrate these three types, as well as others. The three types are the lack-of-knowledge inference, the functional analogy, and the spatial superpart inference.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Because", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "They are all common inferences and serve to illustrate the different kinds of inferences in the theory.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Because", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The formal analysis of the protocols attempts to specify all the underlying inferences that the subject was using in his response.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Because", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "For the inferences that bear directly on the question, I have marked whether they are evidence for a negative or positive answer.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Because", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Where a premise was not directly stored, but derived from another inference, I have indicated the inference from which it is derived.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Because", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "I have indicated the approximate degree of certainty by marking the conclusion with \"Maybe\", \"Probably\", or leaving it unmarked.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Because", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Where a subject may be making a particular inference which the protocol does not clearly indicate, I have marked the inference ,possible\". Separating inferences in this manner is oversimplified, but has the virtue of being understandable.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Because", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The lack-of-knowledge inference is the most common of all the meta-inferences. The 'protocol I selected to show the lack-of-knowledge inference shows the subject using a variety of meta-inferences to reach an initial conclusion which he then backs off a bit.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Lack-of-Knowledge Inference", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "River?", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Q. Is the Nile longer than the Mekong", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "JB. I think so.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Q. Is the Nile longer than the Mekong", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "JB.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Q.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Why?", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Q.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Because (pause) in junior high I read a book on rivers and I kept looking for the Hudson River because that was the river I knew about and it never appeared, and the Amazon was in there and the Nile was in there and all these rivers were in there, and they were big, and long, and important.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Q.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The Mekong wasn't in there. (pause) It could be just... Q. So therefore, it is not important.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Q.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "It could be Just an American view.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "JB. That's right.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "At that time the Mekong wasn't so important.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "JB. That's right.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Underlying Inferences Functional Abduction on Importance Level (Possible) The importance of a river depends in part on how long it is Th_e_Nile is very important Probablythe Nile is extremely long Meta-Induction From Cases I know the Amazon is extremely long I know the Nile is extremely long (from I) I would know the Mekong is extremely long if it were 3)", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "2)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Lack-of-Knowledge Inference I don't know the Mekong is extremely long I would know the Mekong is extremely long if it were (from 2) Probably the Mekong is not extremely long tying length to importance. He seems to know that importance depends in part on length, and since he assigns different degrees of importance to the Nile and the Mekong, he must be using that in part to infer that the Mekong is not as long as the Nile. There also is a meta-induction he is making: that since he knows the Amazon and the Nile are very long, he would know the Mekong is long if it were.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "This meta-induction is acting on one of the certainty conditions for the L lack-of-knowledge inference: the more similar cases stored with the given property, the more certain the inference. Taken together, these inferences make the lack-of-knowledge inference very certain.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "However at the end the subject backs off his conclusion because he finds another chain of reasoning that makes him less certain (inferences 6 and 7). from America. Based on this the subject realizes that the Mekong's lack of importance may be due to this remoteness rather than its shortness in length.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "His reasoning then depends on his notion of what alternative factors importance depends on, and how it might mislead him in this case.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "So this chain of reasoning is also acting on the certainty conditions affecting the lack-of-knowledge inference, but in the opposite direction from the other meta-inferenees.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The rule for a lack-of-knowledge inference is shown in the table below. It generally has the form: If it were true, I would know about it; I don't, so it must not be true.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "It is computed by comparing the importance level of the proposition in question against the depth of knowledge about the concepts involved Gentner & Collins, 1978) .", | |
| "cite_spans": [ | |
| { | |
| "start": 139, | |
| "end": 163, | |
| "text": "Gentner & Collins, 1978)", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Lack-of-Knowledge Inference I) If a person would know about a property for a given set if it were in a given range, and 2) if the person does not know about that property, 3) then infer that the property is not in the given range for that set. Example If Kissinger were 6'6\" tall, I would know he is very tall. I don't, so he must not be that tall.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Conditions that increase certainty: I) The more important the particular set.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "2) The less likely the property is in the given range.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "3) The more information stored about the given set. 4) The more similar properties stored about the given set. 5) The more important the given property. 6) The more information stored about the given property. 7) The more similar sets stored that have the given property.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The conditions affecting the certainty of a lack-of-knowledge inference can be illustrated by the example in the table: I) Condition I refers to the importance of the given set.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In the example Kissinger is quite important, so one is more likely to know whether he is 6'6\" than whether Senator John Stennis is 6' @' for example. 2) Condition 2 refers to the likelihood that the property is in the given range. Likelihood affects the inference in two ways: low likelihood makes a negative inference more certain a priori, and low likelihood also makes a property more unusual and therefore more likely to come to a person's attention.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "For example, it is less likely that Kissinger is 7' 2\" than 6' 6\", because 7' 2\" is more unusual. If Kissinger were a basketball player, on the other hand, his being 6' 6\" would not be unusual at all. 3) Condition 3 relates to the depth-of-knowledge about the given set. The more one knows about Kissinger, the more certainly one would know that he is 6' 6\", if he is. 4) Condition 4 relates to the number of similar properties stored about the set (i.e. the relatedness of the information known about the set).", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "If one knows a lot about Kissinger's physical appearance, one feels more certain one would know he is extremely tall, if he is. 5) Condition 5 relates to the importance of the particular property. Being extremely tall isn't as important as missing a leg say, so people are more likely to know if Kissinger is missing a leg. 6) Condition 6 relates to the depth-of-knowledge about the particular property.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "For example, a person who has particular expertise about the physical stature of people is more likely to know that Kissinger is extremely tall, if he is. 7) Condition 7 relates to the number of similar sets known to have the given property.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "For example, if one knows that Ed Muskie and Tip O'Neil are unusually tall, then one ought to know that Kissinger is unusually tall, if in fact he is 6' 6\".", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "5)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The initial protocol on coffee growing in the Llanos illustrated two functional inferences: a functional calculation concerning rainfall, and a functional analogy between the Brazilian savanna and the Llanos. One of the more common functional inferences is the functional analogy.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Functional Analogy", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The protocol I selected to illustrate it contrasts the use of a simple analogy and a functional analogy.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Functional Analogy", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "BF. No, a goose -Well, its like a duck, but its not a duck.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Q. Can a goose quack?", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "It can honk, but to say it can quack.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Q. Can a goose quack?", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "No, I think its vocal cords are built differently.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Q. Can a goose quack?", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "They have a beak and everything, but no, it can't quack.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Q. Can a goose quack?", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A goose is similar to a duck A duck quacks Maybe a goose quacks 2) Importance-Level Inequality (Possible) I know a goose honks Quacking is as important as honking Probably I would know about a goose quacking if it did 3) Lack-of-Knowledge Inference (Negative Evidence) (Possible) I don't know that a goose quacks I would know about a goose quacking if it did (from 2) Probably a goose doesn't quack 4) Negative Functional Analogy (Negative Evidence) The sound a bird makes depends on its vocal cords A goose is different from a duck in its vocal cords A duck quacks Probably a goose doesn't quack", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 430, | |
| "end": 450, | |
| "text": "(Negative Evidence)", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Underlying Inferences I) Simple Analogy (Positive Evidence)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The simple analogy, which is based on a match of all the properties of ducks and geese, leads to the possible conclusion that a goose can quack, because a duck quacks. This inference shows up in the reference to \"its like a duck\" and in the uncertainty of the negative conclusion the student is drawing. It is positive evidence and only shows up to the degree it argues against the general negative conclusion. The importance-level inequality and lack-of-knowledge inference are suggested by the sentence \"It can honk, but to say it can quack.\"", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Underlying Inferences I) Simple Analogy (Positive Evidence)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Here knowledge about honking seems to imply that a goose doesn't quack.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Underlying Inferences I) Simple Analogy (Positive Evidence)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "I would argue that such an inference has to involve the lack-of-knowledge inference, since it is possible that a goose might sometimes honk and sometimes quack.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Underlying Inferences I) Simple Analogy (Positive Evidence)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The functional analogy is apparent in the concern about vocal cords, which the subject thinks are the functional determinants of the sounds made.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Underlying Inferences I) Simple Analogy (Positive Evidence)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "I think the sound is determined by the length of the neck, which is probably what the subject was thinking of. Honking may just be quacking resonated through a longer tube.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Underlying Inferences I) Simple Analogy (Positive Evidence)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "But in any case, the mismatch the subject finds on the relevant factor leads to a negative conclusion which supports the lack-of-knowledge inference.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Underlying Inferences I) Simple Analogy (Positive Evidence)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The table shows the rule for a functional analogy.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Underlying Inferences I) Simple Analogy (Positive Evidence)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Functional Analog\u00a5 I) If a dependent variable depends on a number of independent variables, and 2) if one set matches another set on the independent variables, and 3) if the value of the dependent variable for one set is in a.given range, 4) then infer that the value of the dependent variable for the other set is in the given range.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Underlying Inferences I) Simple Analogy (Positive Evidence)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The Brazilian savanna is like Llanos in its temperature, rainfall, soil, and vegetation.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Example", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Thus, if the Brazilian savanna produces coffee, then the Llanos ought to also.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Example", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "CQnditions that increase certainty: I) The more independent variables on which the two sets match, and the fewer on which they mismatch.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Example", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "2) The greater the dependency on any independent variables on which the two sets match, and the less the dependency on any independent variables that mismatch.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Example", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "3) The better the match on any independent variable. 4) The greater the dependency on those independent variables that match best. 5) The more certain the dependent variable is in the given range for the one set. 6) The more likely the value of the dependent variable is in the given range a priori. 7) The more certain the independent variables are in the given ranges for both sets.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Example", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "I can illustrate the different certainty conditions for a functional analogy in terms of the example in the table: I) Condition I refers to the number of factors on which the two sets match. If the two regions match only in climate and vegetation, that would be less strong evidence that they produce the same products than if they match on all four variables. 199 2) Condition 2 refers to the degree the dependent variable depends on different factors that match or mismatch. Coffee growing depends more on temperature and rainfall than on soil or vegetation. Thus a match on these first two factors makes the inference more certain than a match on the latter two factors. 3) Condition 3 relates to the quality of the match on any factor. The better the match with respect to temperature, rainfall, etc.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Example", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "the more certain the inference. 4) Condition 4 refers to the degree of dependency on those factors that match best.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Example", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A good match with respect to the rainfall pattern leads to more certainty than a good match with respect to the vegetation. 5) Condition 5 relates to the certainty that the property is in the given range for the first set. The more certain one is that the Brazilian savanna produces coffee, the more certain the inference. 6) Condition 6 relates to the a priori likelihood that the property will be in the given range.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Example", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The more likely that any region grows coffee, the more certain the inference. 7) Condition 7 relates to the certainty that the factors are in the given ranges for both sets.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Example", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "For example, the more certain that both savannas have the same temperature, etc., the more certain the inference.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Example", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The theory assumes that spatial inferences are made by constructing an image of the concepts involved, and making various computations on that image (Collins & Warnock, 1974; Kosslyn & Schwartz, 1977) .", | |
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| { | |
| "start": 149, | |
| "end": 174, | |
| "text": "(Collins & Warnock, 1974;", | |
| "ref_id": "BIBREF3" | |
| }, | |
| { | |
| "start": 175, | |
| "end": 200, | |
| "text": "Kosslyn & Schwartz, 1977)", | |
| "ref_id": "BIBREF6" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Spatial Superpart Inferenc~", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "An example of a spatial inference occurred in the earlier protocol about coffee growing, when the respondent concluded that a savanna might be used for growing coffee because he thought the coffee growing region around Sao Paulo might overlap the Brazilian savanna.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Spatial Superpart Inferenc~", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "This spatial matching process, which occurs in a variety of protocols, involves constructing a spatial image with both concepts in it, and finding their spatial relationship (e.g., degree of overlap, relative size or direction) from the constructed image.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Spatial Superpart Inferenc~", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The ", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Spatial Superpart Inferenc~", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Tollens (Positive evidence) (possible) The Pacific coast misconception depends on the inland place being north of the coastal place. Seattle is on the coast. Texas is inland. Texas is south of Seattle. The Pacific coast misconception does not apply to Texas and Seattle.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In the protocol the subject constructs a line from Washington to Texas for the purpose of evaluating its slope. The constructed line does slope east, so he answers yes. Implicit in this protocol is a spatial subpart inference or spatial deduction, that Seattle is part of Washington and the slope of the line found earlier applies to Seattle. This kind of subpart inference was found to show up in response time by Stevens (1976) .", | |
| "cite_spans": [ | |
| { | |
| "start": 415, | |
| "end": 429, | |
| "text": "Stevens (1976)", | |
| "ref_id": "BIBREF13" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The subject briefly reconsidered his conclusion because he thought of the \"Pacific Coast Misconception,\" that people mistakenly think that places inland are always east of places on the coast.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
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| { | |
| "text": "By the meta-analogy in 3, he inferred that maybe Seattle-Texas was like San Diego-Las Vegas in that the inland location was west of the coastal location. But the subject ruled out the analogy by some inference such as that shown in 4. Actually, the functional modus tollens in 4 hides the spatial processing that the subject probably used to rule out the analogy in 3.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Probably, he knew that the reason for the \"Pacific Coast Misconception\" has to do with the southeasterly slant of the Pacific coast. By knowing that, you can figure out that the misconception depends on the inland location being north of the coastal location.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "I have finessed the spatial reasoning process by stating that conclusion as a premise in 4.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The next table shows the rule for a spatial superpart inference (or spatial deduction).", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Spatial Sunerpart Inference I) If a property is in a given range for some set, and 2) if another set is a subpart of that set, 3) then infer that the property is in that range for the subpart.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Example It is raining in New England and Boston is in New England. Therefore it may be raining in Boston.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Conditions that increase certaintv: I) The more central the subpart is to the set.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "2) The greater the average spatial extent of the property. 3) The greater the distance of the nearest set with a contradictory property. 4) The greater the extent of the subpart within the set. 5) The more likely a priori that the property is in the given range for the subpart. 6) The more certain the property is in the given range for the set.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The certainty conditions can be illustrated in terms of the example in the table: I) Condition 1 relates to the centrality of the subpart. For example, if it's raining in New England it is more likely to be raining in Massachusetts than Maine because Massachusetts is more central. 2) Condition 2 relates to whether the property tends to be spatially distributed or not. For example, rain tends to be distributed over smaller areas than electric service, so it is a less certain inference that it is raining in Maine than that there is electric service in Maine, given that the property applies to New England. 3) Condition 3 relates to the distance to the nearest concept with a contradictory property.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "For example, if you know it's not raining in New Brunswick, that is stronger evidence against it's raining in Maine than if it's not raining in Montreal. Condition 4 relates to the extent of the subpart.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "For example, if it's raining in New England it is more likely to be raining in Rhode Island than in Boston, because Rhode Island is larger. 5) Condition 5 relates to the a priori likelihood of the property, for example, if it's raining in Washington State, it's more likely to be raining in Seattle than in Spokane because Seattle gets more rain on the average. 6) Condition 6 relates to the person's certainty that the property holds for the concept.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "For example, the more certain the person is that it is raining in New England, the more certain that it's raining in Boston.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Modus", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The theory I am developing is based on these and similar analyses of a large number of human protocols. Because the same inference types recur in many different answers, it is possible to abstract the systematic patterns in the inferences themselves, and many of the different conditions that affect people's certainty in using different inference types.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "CONCLUSION", | |
| "sec_num": null | |
| } | |
| ], | |
| "back_matter": [], | |
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