Partial Logic as a Logic of Extensional Alethic Modality

Time and Modality in Avicennan Logic

Proofs and Expressiveness in Alethic Modal Logic

The above dictionary characterization of alethic modalities states the central notions of alethic modal logic: necessity, and other notions that are usually thought of as being definable in terms of necessity and Boolean negation: impossibility, contingency, and possibility. The syntax of modal propositional logic is inductively defined over a denumerable set of sentence letters p0, p1, p2, . ....

Extensional vs. Intensional Logic

The German mathematician and one of the founding fathers of modern logic, Gottlob Frege (1848-1925), was the first to clearly realize that semantics has little to do with psychology, and that it could be usefully explicated in mathematical terms (see Dummett, 1973; 1981). His depsychologization of semantics followed from his depsychologization of logic. Frege understood how crucial it was for t...

The Logic of Extensional RDFS

The normative version of RDFS gives non-standard (intensional) interpretations to some standard notions such as classes and properties. In this paper we develop the extensional semantics for the RDFS vocabulary, which surprisingly preserves the simplicity and computational complexity of deduction of the intensional case. This result will impact current implementations in a positive sense, as re...

De re and De dicto Modality in Islamic Traditional Logic