The exegesis of canonical philosophical texts – mostly Plato and Aristotle was part parcel the late antique way doing philosophy. This led to a rich tradition commentaries for related purposes teaching research. syllogistic presentation arguments contained in source often considered as an important commentator’s job. Often, but not always, reconstruction used demonstrate consistency logical cog...

Entailment relations are of central importance in the enterprise of natural language semantics. In modern logic, entailment relations are characterized from two viewpoints: the modeltheoretic and proof-theoretic ones. By contrast, most approaches to formalizing entailment relations in natural languages have been solely based on model-theoretic conceptions. Thus, the notion of validity is only c...

In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of some recently proposed proof-systems for these logics.

This paper is a note on a very simple and elementary fact having to do with reasoning about relations. The kinds of reasoning that we have in mind come from two different areas: extended syllogistic logics and description logics. In extended syllogistic logic, one wants to reason about terms formed from binary relations and terms. We illustrate with some examples from the recent paper van Rooij...

This is another contribution to the unending controversy over two Barbaras. My approach problem hopefully quite new: I wish view issue through prism of modal upgrading. Modal upgrading occurs when a subject term that has only been predicated assertorically in premises apodictically either: i) conclusion given syllogism, or; ii) some proposition derived from either syllogism alone or combination...

In the first book of Prior Analytics, Aristotle sets out, for time in Greek philosophy, a logical system. After this, compares this method with Plato’s division, procedure designed to find essences natural kinds through systematic classification. This critical comparison APr I.31 raises an interpretive puzzle: how can reasonably juxtapose two methods that differ so much their aims and approach?...

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.