Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers ∀p, ∃p over propositions. In the context of Kripke semantics, a proposition is a subset of the worlds in a model structure which is upward closed, i.e., if h ∈ P , then h ∈ P for all h ≤ h. For propositional intuitionistic logic H, several classes of model structures are known...

The role of classical (Tarskian) semantics within logic-based Knowledge Representation has come under attack even from some within the symbolic AI camp, for example McDermott ((McD87]) and Kowalski ((Kow93]). The alternative seems to be some more procedural account of the meaning of the logical formalisms used and the operations based on it. In neither case is the alternative suuciently worked ...

Introduction. This is a sequel to our article “Predicative foundations of arithmetic” (1995), referred to in the following as [PFA]; here we review and clarify what was accomplished in [PFA], present some improvements and extensions, and respond to several challenges. The classic challenge to a program of the sort exemplified by [PFA] was issued by Charles Parsons in a 1983 paper, subsequently ...

Late TwenCen philosophical theories of concepts confine their movements within a surprisingly constrained Carnapian compass. Already in the Aufbau, Carnap had pictured empirical concepts as having contents that were both on the one hand derived from perceptual experience and on the other articulated by their logical form. Quine is a direct descendant of this tradition. But these two broad dimen...

The aim of this paper is to motivate and defend a conventional approach to assertion and other illocutionary acts. Such an approach takes assertions, questions and orders to be moves within an essentially rule-governed activity similar to a game. The most controversial aspect of a conventional account of assertion is that according to it, for classifying an utterance as an assertion, question o...

General-elimination harmony articulates Gentzen’s idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the...

The meaning of a declarative sentence and that of an interrogative sentence differ in their aspect of mood. A semantics of mood has to account for the differences in meaning between these sentences, and it also has to explain that sentences in different moods may have a common core. The meaning of the declarative mood is to be explained not in terms of actual force (contra Dummett), but in term...

The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the proof-theoretical prominency of intuitionistic logic, the forthcoming answer is that it is this logic that is the obvious choice for the accolade. Though there is little doubt that this choice is correc...

In addition to introducing the very successful product line of conversational implicatures, Paul Grice and his successors have assembled an arguably inchoate class of phenomena under the trade name of CONVENTIONAL IMPLICATURE, whose reception in the scholarly marketplace has been somewhat bridled. A conventional implicature associated with expression E is a non-cancelable contribution to the co...

Formal systems of fuzzy logic (including the well-known à Lukasiewicz and Gödel-Dummett infinite-valued logics) are well-established logical systems and respected members of the broad family of the so-called substructural logics closely related to the famous logic BCK. The study of fragments of logical systems is an important issue of research in any class of nonclassical logics. Here we study ...