à Lukasiewicz had every reason to suppose that Leibniz’s winged Calculemus! had been connected with the Aristotelian syllogistic [4, § 34]. Indeed, after Louis Couturat’s pioneer efforts in commenting and publishing Leibniz’s logical opuscula ([1], [2]). The basic idea of the arithmetization of syllogistic was to establish a correspondence between terms and suitable integers (the characteristic...

Traditional syllogisms involve sentences of the following simple forms: All X are Y , Some X are Y , No X are Y ; similar sentences with proper names as subjects, and identities between names. These sentences come with the natural semantics using subsets of a given universe, and so it is natural to ask about complete proof systems. Logical systems are important in this area due to the prominenc...

The phenomenon of belief bias in syllogistic reasoning occurs when the a priori believability of a conclusion influences the intuitive acceptability of that conclusion. Prior beliefs about the world can be formalized into a probabilistic generative model of situations. Tessler and Goodman (2014) proposed that this very idea can account for the range of acceptabilities of conclusions from catego...

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an "immediate inference" task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (...

A recent meta-analysis carried out by Khemlani and Johnson-Laird showed that the conclusions drawn by humans in psychological experiments about syllogistic reasoning deviate from the conclusions drawn by classical logic. Moreover, none of the current cognitive theories predictions fit the empirical data. In this paper a Computational Logic analysis clarifies seven principles necessary to draw t...

Classical syllogistic reasoning, also known as Aristotelian reasoning, is of particular interest in cognition. Such reasoning, which can seem simple at first, is known to be associated with high error rates. Although some research has been done on this topic, the underlying mechanisms used by human beings remain largely unknown. To understand the underlying cognitive properties associated with ...

Pratt and Third’s syllogistic fragments of English can be used to capture, in addition to syllogistic reasoning, many other kinds of common sense reasoning, and, in particular (i) knowledge base consistency and (ii) knowledge base query answering, modulo their FO semantic representations. We show how difficult, in terms of semantic (computational) complexity and data complexity (i.e., computati...

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...