The explanatory power of logic is vast and therefore it has proved a valuable tool for many disciplines, including the building-blocks of cognitive science, such as philosophy, computer science, mathematics, artificial intelligence, and linguistics. Logic has a great track record in providing interesting insights by means of formalization, and as such it is very useful in disambiguating psychological theories. Logically formalized cognitive theories are not only the source of unequivocal experimental hypotheses, but they also lend themselves naturally to computational modeling. (...) Most importantly, modern logic has at its service a rich variety of tools to assess and compare such psychological theories. This toolbox can be utilized in evaluating cognitive models along the following dimensions:logical relationships, for example, incompatibility or identity of models;explanatory power, for example, what can be expressed by means of a model?computational plausibility, for example, a. (shrink)

This paper explores the question of what makes diagrammatic representations effective for human logical reasoning, focusing on how Euler diagrams support syllogistic reasoning. It is widely held that diagrammatic representations aid intuitive understanding of logical reasoning. In the psychological literature, however, it is still controversial whether and how Euler diagrams can aid untrained people to successfully conduct logical reasoning such as set-theoretic and syllogistic reasoning. To challenge the negative view, we build on the findings of modern diagrammatic logic and introduce (...) an Euler-style diagrammatic representation system that is designed to avoid problems inherent to a traditional version of Euler diagrams. It is hypothesized that Euler diagrams are effective not only in interpreting sentential premises but also in reasoning about semantic structures implicit in given sentences. To test the hypothesis, we compared Euler diagrams with other types of diagrams having different syntactic or semantic properties. Experiment compared the difference in performance between syllogistic reasoning with Euler diagrams and Venn diagrams. Additional analysis examined the case of a linear variant of Euler diagrams, in which set-relationships are represented by one-dimensional lines. The experimental results provide evidence supporting our hypothesis. It is argued that the efficacy of diagrams in supporting syllogistic reasoning crucially depends on the way they represent the relational information contained in categorical sentences. (shrink)

Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms of regions as in (...) the standard approach, but in terms of topological relations between diagrammatic objects. We formalize the unification rule, which plays a central role in Euler diagrammatic reasoning, in a style of natural deduction. We prove the soundness and completeness theorems with respect to a formal set-theoretical semantics. We also investigate structure of diagrammatic proofs and prove a normal form theorem. (shrink)

This paper contains two traditions of diagrammatic studies namely one, the Euler–Venn–Peirce diagram and the other, following tradition of Aristotle, the square of oppositions. We put together both the traditions to study representations of singular propositions, their negations and the inter relationship between the two. Along with classical negation we have incorporated negation of another kind viz. absence. We have also considered the changes that take place in the context of open universe.