In this paper we present a new fast tableau-based decision procedure for the ground set-theoretic fragment Multi-Level Syllogistic with Singleton (in short MLSS) which avoids the interleaving of model checking steps. The underlying tableau calculus is based upon the system KE.

In this study, Johnson-Laird and his colleagues’ mental model reasoning is formally analyzed as a non-sentential reasoning. Based on the recent developments in implementations of mental model theory, we formulate a mental model reasoning for syllogistic fragments in a way satisfying the requirement of formal specification such as mental model definition.

In this paper we present a unifying discrete framework for various representation theorems in the field of spatial reasoning. We also show that the universal and existential quantifiers of restricted scope used in first order languages and represented as binary relations in the syllogistic algebras considered in [12] may be studied in this framework.

The purpose of this study was to examine the relation between working memory span and syllogistic reasoning performance. In addition, performance for the reasoning task was compared to predictions made by mental model theory and the probability heuristics model. According to mental model theory, syllogisms that require the use of more mental models are more difficult. According to the probabili...

Parry discusses an extension of Aristotle’s syllogistic that uses four nontraditional quantifiers. We show that his conjectured decision procedure for validity for the extended syllogistic is correct even if syllogisms have more than two premises. And we axiomatize this extension of the syllogistic. 1 Background and motivation Parry [2] discusses an extension of the syllogistic in which sentenc...

Abduction and induction are reasoning forms for drawing conclusions from incomplete information. Induction, i.e. inferring properties of sets of individuals from properties of individuals, was already distinguished by Aristotle, while the term ‘abduction’ was introduced much later by Peirce for inference of explanations for observed phenomena. Both reasoning forms are presently being studied an...