First-order Logic: Modality and Intensionality

Contemporary use of the term ’intension’ derives from the traditional logical Frege-Russell’s doctrine that an idea (logic formula) has both an extension and an intension. Although there is divergence in formulation, it is accepted that the extension of an idea consists of the subjects to which the idea applies, and the intension consists of the attributes implied by the idea. From the Montague’s point of view, the meaning of an idea can be considered as particular extensions in different possible worlds. In this paper we analyze the minimal intensional semantic enrichment of the syntax of the FOL language, by unification of different views: Tarskian extensional semantics of the FOL, modal interpretation of quantifiers, and a derivation of the Tarskian theory of truth from unified semantic theory based on a single meaning relation. We show that not all modal predicate logics are intensional, and that an equivalent modal Kripke’s interpretation of logic quantifiers in FOL ...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Zoran Majkic
• Keywords: CORR 2011, Education, Intensional Semantics, Logic, Semantics