Socratic Proofs and Paraconsistency: A Case Study

This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φ_v. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.     

The seven virtues of simple type theory

Simple type theory, also known as higher-order logic, is a natural extension of first-order logic which is simple, elegant, highly expressive, and practical. This paper surveys the virtues of simple type theory and attempts to show that simple type theory is an attractive alternative to first-order logic for practical-minded scientists, engineers, and mathematicians. It recommends that simple type theory be incorporated into introductory logic courses offered by mathematics departments and into the undergraduate curricula for computer science and software engineering students.     

A logical formalization of the OCC theory of emotions

In this paper, we provide a logical formalization of the emotion triggering process and of its relationship with mental attitudes, as described in Ortony, Clore, and Collins’s theory. We argue that modal logics are particularly adapted to represent agents’ mental attitudes and to reason about them, and use a specific modal logic that we call Logic of Emotions in order to provide logical definitions of all but two of their 22 emotions. While these definitions may be subject to debate, we show that they allow to reason about emotions and to draw interesting conclusions from the theory.     

Open answer set programming for the semantic web

We extend answer set programming (ASP) with, possibly infinite, open domains. Since this leads to undecidable reasoning, we restrict the syntax of programs, while carefully guarding knowledge representation mechanisms such as negation as failure and inequalities. Reasoning with the resulting extended forest logic programs (EFoLPs) can be reduced to finite answer set programming, for which reasoners are available.We argue that extended forest logic programming is a useful tool for uniformly representing and reasoning with both ontological and rule-based knowledge, as they can capture a large fragment of the OWL DL ontology language equipped with DL-safe rules. Furthermore, EFoLPs enable nonmonotonic reasoning, a desirable feature in locally closed subareas of the Semantic Web.     

The Concurrent,Continuous Fluent Calculus

The Fluent Calculus belongs to the established predicate calculus formalisms for reasoning about actions. Its underlying concept of state update axioms provides a solution to the basic representational and inferential Frame Problems in pure first-order logic. Extending a recent research result, we present a Fluent Calculus to reason about domains involving continuous change and where actions occur concurrently.     

Implicit connectives of algebraizable logics

An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all connectives defined implicitly by axiomatic extensions of the logic are explicitly definable.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko