Modeling Human Syllogistic Reasoning: The Role of “No Valid Conclusion” (original) (raw)

A Computational Logic Approach to Human Syllogistic Reasoning

Cognitive Science, 2017

A recent meta-analysis (Khemlani & Johnson-Laird, 2012) about psychological experiments of syllogistic reasoning demonstrates that the conclusions drawn by human reasoners strongly deviate from conclusions of classical logic. Moreover, none of the current cognitive theories predictions fit reliably the empirical data. In this paper, we show how human syllogistic reasoning can be modeled under a new cognitive theory, the Weak Completion Semantics. Our analysis based on computational logics identifies seven principles necessary to draw the inferences. Hence, this work contributes to a computational foundation of cognitive reasoning processes.

Improving Cognitive Models for Syllogistic Reasoning

2020

Multiple cognitive theories make conflicting explainations for human reasoning on syllogistic problems. The evaluation and comparison of these theories can be performed by conceiving them as predictive models. Model evaluation often employs static sets of predictions rather than full implementations of the theories. However, most theories predict different responses depending on the state of their internal parameters. Disregarding the theories’ capabilities to adapt parameters to different reasoners leads to an incomplete picture of their predictive power. This article provides parameterized algorithmic formalizations and implementations of some syllogistic theories regarding the syllogistic single-response task. Evaluations reveal a substantial improvement for most cognitive theories being made adaptive over their original static predictions. The best performing implementations are PHM, mReasoner and Verbal Models, which almost reach the MFA benchmark. The results show that there e...

Do Models Capture Individuals? Evaluating Parameterized Models for Syllogistic Reasoning

2020

The prevailing focus on aggregated data and the lacking groupto-individual generalizability it entails have recently been identified as a major cause for the low performance of cognitive models in the field of syllogistic reasoning research. This article attempts to add to the discussion about the performance of current syllogistic reasoning models by considering the parameterization capabilities some cognitive models offer. To this end, we propose a model evaluation setting targeted specifically toward analyzing the capabilities of a model to fine-tune its inferential mechanisms to individual human reasoning data. This allows us to (1) quantify the degree to which models are able to capture individual human reasoning behavior, (2) analyze the efficiency of the parameters used by models, and (3) examine the functional differences between the prediction capabilities of competing models on a more detailed level. We apply this method to two state-of-the-art models for syllogistic reaso...

A Syllogistic Reasoning Theory and Three Examples

2015

A recent meta-study shows that the conclusions driven by human reasoners in psychological experiments about syllogistic reasoning are not the conclusions predicted by classical first-order logic. Moreover, current cognitive theories deviate significantly from the empirical data. In the following, three important cognitive approaches are presented and compared to predictions made by a new approach to model human reasoning tasks, viz. the weak completion semantics. Open questions and implications are discussed.

The Probability Heuristics Model of Syllogistic Reasoning

Cognitive Psychology, 1999

A probability heuristic model (PHM) for syllogistic reasoning is proposed. An informational ordering over quantified statements suggests simple probability based heuristics for syllogistic reasoning. The most important is the ''min-heuristic'': choose the type of the least informative premise as the type of the conclusion. The rationality of this heuristic is confirmed by an analysis of the probabilistic validity of syllogistic reasoning which treats logical inference as a limiting case of probabilistic inference. A meta-analysis of past experiments reveals close fits with PHM. PHM also compares favorably with alternative accounts, including mental logics, mental models, and deduction as verbal reasoning. Crucially, PHM extends naturally to generalized quantifiers, such as Most and Few, which have not been characterized logically and are, consequently, beyond the scope of current mental logic and mental model theories. Two experiments confirm the novel predictions of PHM when generalized quantifiers are used in syllogistic arguments. PHM suggests that syllogistic reasoning performance may be determined by simple but rational informational strategies justified by probability theory rather than by logic. who will also provide full mathematical derivations of the notion of ''probabilistic validity '' employed in this article. 191

Multinomial Processing Models for Syllogistic Reasoning: A Comparison

Cognitive Science, 2018

To this day, a great variety of psychological theories of reasoning exist aimed at explaining the underlying cognitive mechanisms. The high number of different theories makes a rigorous comparison of cognitive theories necessary. The present article proposes to use Multinomial Processing Trees to compare two of the most prominent theories of syllogistic reasoning: the Mental Models Theory and the Probability Heuristics Model. For this, we reanalyzed data from a meta-analysis on six studies about syllogistic reasoning. We evaluate both models with respect to their overall fit to the data by means of G2, AIC, BIC, and FIA, and on a parametric level. Our comparison indicates that a MMT-variant, though having more parameters, is slightly better on all criteria except of the BIC. Yet, none of the two models, realized as MPTs, is clearly superior. We outline the impact of the different theoretical principles and discuss implications for modeling syllogistic reasoning.

Cognitive Uncertainty in Syllogistic Reasoning: An Alternative Mental Models Theory

2001

In this paper we propose a mental models theory of syllogistic reasoning which does not incorporate a falsification procedure and clearly specifies which conclusions will be generated and in what order of preference. It is assumed the models constructed vary in terms of the number of uncertain representations of end terms, and the directness of the representation of the subjects of valid conclusions. These key factors determine which quantified conclusion will be generated, as well as the varying tendency to respond that "nothing follows". The theory is shown to provide a close fit to meta-analysis data derived from past experiments.

Unifying Models for Belief and Syllogistic Reasoning

2021

Judging if a conclusion follows logically from a given set of premises can depend much more on the believability than on the logical validity of the conclusion. This so-called belief bias effect has been replicated repeatedly for many decades now. An interesting observation is, however, that process models for deductive reasoning and models for the belief bias have not much of an overlap - they have largely been developed independently. Models for the belief bias often just implement first order logic for the reasoning part, thereby neglecting a whole research field. This paper aims to change that by presenting a first attempt at substituting the first order logic components of two models for belief, selective scrutiny and misinterpreted necessity, with two state of the art approaches for modeling human syllogistic reasoning, mReasoner and PHM. In addition, we propose an approach for extending the traditionally dichotomous predictions to numerical rating scales thereby enabling more...

Inhibitory mechanism of the matching heuristic in syllogistic reasoning

Acta Psychologica, 2014

A number of heuristic-based hypotheses have been proposed to explain how people solve syllogisms with automatic processes. In particular, the matching heuristic employs the congruency of the quantifiers in a syllogismby matching the quantifier of the conclusion with those of the two premises. When the heuristic leads to an invalid conclusion, successful solving of these conflict problems requires the inhibition of automatic heuristic processing. Accordingly, if the automatic processing were based on processing the set of quantifiers, no semantic contents would be inhibited. The mental model theory, however, suggests that people reason using mental models, which always involves semantic processing. Therefore, whatever inhibition occurs in the processing implies the inhibition of the semantic contents. We manipulated the validity of the syllogism and the congruency of the quantifier of its conclusion with those of the two premises according to the matching heuristic. A subsequent lexical decision task (LDT) with related words in the conclusion was used to test any inhibition of the semantic contents after each syllogistic evaluation trial. In the LDT, the facilitation effect of semantic priming diminished after correctly solved conflict syllogisms (match-invalid or mismatch-valid), but was intact after no-conflict syllogisms. The results suggest the involvement of an inhibitory mechanism of semantic contents in syllogistic reasoning when there is a conflict between the output of the syntactic heuristic and actual validity. Our results do not support a uniquely syntactic process of syllogistic reasoning but fit with the predictions based on mental model theory.

A Mixed Rasch Model of Dual-Process Conditional Reasoning Draft June 1, 2006 - Please do not quote

A fine-grained dual-process approach to conditional reasoning is advocated: Responses to conditional syllogisms are reached through the operation of either one of two systems, each of which can rely on two different mechanisms. System1 relies either on pragmatic implicatures or on the retrieval of information from semantic memory; System2 operates first through inhibition of System1, then (but not always) through activation of analytical processes. It follows that reasoners will fall into one of four groups of increasing reasoning ability, each group being uniquely characterized by (a) the modal pattern of individual answers to blocks of affirming the consequent, denying the antecedent, and modus tollens syllogisms featuring the same conditional; and (b) the average rate of determinate answers to , , and . This account receives indirect support from the extant literature, and direct support from a mixed Rasch model of responses given to 18 syllogisms by 486 adult reasoners.