Prolegomena of a Logic of Causality and Dynamism

We present in this article a new logical system inspired from linear logic. This system is designed in order to express causality and dynamism. The cut elimination theorem holds for this logic. Examples of applications are given.     

On Kripke’s Dogmatism Paradox: A Logical Dynamical Analysis

As a byproduct of solving the surprise-exam paradox, Saul Kripke formulates a “dogmatism paradox” which seems to show that knowledge entails dogmatism. In this paper, the author analyzes the nature of the dogmatism paradox from a logical dynamical perspective. The author suggests that the dogmatism paradox is better understood as a paradox of knowledge attribution rather than of knowledge. Therefore, the dogmatism paradox could be solved without sacrificing the principle of epistemic closure. Based on a famous version of relevant alternatives theory, the author formalizes a logic of knowledge attribution in the style of logical dynamics, namely, public retraction logic, and analyzes how knowledge attributions are retracted with the expansion of relevant alternatives.     

A Modal Sortal Logic

An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system is formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system.     

Separating the wheat from the chaff: does discriminating between diagnostic and nondiagnostic information eliminate the dilution effect?

The dilution effect refers to the finding that judgments are often unduly influenced by nondiagnostic information, producing regressive judgment. Because the dilution effect is a problem in various domains, strategies to control the impact of nondiagnostic information were explored by drawing on a perceptual and a conversational account of the dilution effect. Three experiments (n = 259) demonstrate that explicit instructions to discriminate between diagnostic and nondiagnostic information did not reduce the dilution effect. Rather, consistent with a perceptual explanation but not consistent with a conversational explanation, the dilution effect disappeared only when participants engage in perceptual control, that is, when they actively remove nondiagnostic pieces of information before making a judgment. Copyright © 2004 John Wiley & Sons, Ltd.     

A First Order Nonmonotonic Extension of Constructive Logic

Certain extensions of Nelson's constructive logic N with strong negation have recently become important in arti.cial intelligence and nonmonotonic reasoning, since they yield a logical foundation for answer set programming (ASP). In this paper we look at some extensions of Nelson's .rst-order logic as a basis for de.ning nonmonotonic inference relations that underlie the answer set programming semantics. The extensions we consider are those based on 2-element, here-and-there Kripke frames. In particular, we prove completeness for .rst-order here-and-there logics, and their minimal strong negation extensions, for both constant and varying domains. We choose the constant domain version, which we denote by QN^c₅, as a basis for de.ning a .rst-order nonmonotonic extension called equilibrium logic. We establish several metatheoretic properties of QN^c₅, including Skolem forms and Herbrand theorems and Interpolation, and show that the .rst-oder version of equilibrium logic can be used as a foundation for answer set inference.