Term-Modal Logics

Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators.This gives us a flexible and uniform language for reasoning about the agents themselves and their knowledge. This article gives examples of the expressiveness of the languages and provides sequent-style and tableau-based proof systems for the logics. Furthermore we give proofs of soundness and completeness with respect to the possible world semantics.     

First-order Expressivity for S5-models: Modal vs. Two-sorted Languages

Standard models for model predicate logic consist of a Kripke frame whose worlds come equipped with relational structures. Both modal and two-sorted predicate logic are natural languages for speaking about such models. In this paper we compare their expressivity. We determine a fragment of the two-sorted language for which the modal language is expressively complete on S5-models. Decidable criteria for modal definability are presented.     

Weakly Associative Relation Algebras with Polyadic Composition Operations

In this paper we introduced various classes of weakly associative relation algebras with polyadic composition operations. Among them is the class RWA of representable weakly associative relation algebras with polyadic composition operations. Algebras of this class are relativized representable relation algebras augmented with an infinite set of operations of increasing arity which are generalizations of the binary relative composition. We show that RWA is a canonical variety whose equational theory is decidable.     

Linearization of the BCK-logic

In the paper we obtain a new characterization of the BCK-algebras which are subdirect product of BCK-chains. We give an axiomatic algebraizable extension of the BCK-calculus, by means of a recursively enumerable set of axioms, such that its equivalent algebraic semantics is definitionally equivalent to the quasivariety of BCK-algebras generated by the BCK-chains. We propose the concept of "linearization of a system" and we give some examples.     

The blaze of her splendors: Suggestions about revitalizing fallacy theory

Criticisms of fallacy theory have been lodged from many different directions. In this paper, I consider the classic criticism of incompleteness by DeMorgan, Finocchiaro's claim that fallacies probably exist only in the mind of the interpreter, McPeck's claim that fallacies are at best context-dependent and Paul's complaints about the teaching of fallacies. I seek not merely to defend fallacy theory against unfair criticisms but also to learn from the criticisms what can be done in order to make fallacy theory a viable theory of criticism. I argue that this will involve several changes: rethinking of the nature of fallacy; addressing some theoretical issues; and presenting fallacy theory in a more rigorous fashion. The paper concludes with reflections on how Quine's ontological advice about the resolution of ontological disputes might be applied to the issue of whether or not there are fallacies.     

Rationale for a pragma-dialectical perspective

Starting from a concept of reasonableness as well-consideredness, it is discussed in what way science could serve as a model for reasonable argumentation. It turns out that in order to be reasonable two requirements have to be fulfilled. The argumentation should comply with rules which are both problem-valid and intersubjectively valid. Geometrical and anthropological perspectives don't meet these criteria, but a critical perspective does. It is explained that a pragma-dialectical approach to argumentation which agrees with this critical perspective is indeed problem-valid and that strong pragmatic and utilitarian arguments can be given for its intersubjective validity. Thus, conventional validity is promoted for a code of conduct for discussants who want to resolve their disputes reasonably by way of a critical discussion.     

Woods on Ideals of Rationality in Dialogue

Woods' paper Ideals of Rationality in Dialogue raises six problems for dialogue theory. Woods is right about the seriousness of the problems, but one school of dialogue, that stemming from the work of Charles Hamblin, avoids each of Woods' problems by using commitment instead of belief and by using only immediate logical relations. This paper summarises the reasons Hamblin's school took this course, and explains how Woods' problems are thereby avoided.