by Solomon Feferman Oxford University Press, 1998, 352 pp. $ 60.00 US, ISBN 0195080300 REVIEWED BY ANDREW ARANA Poincaré famously compared the logician’s understanding of mathematics to the understanding we would have of chess if we were only to know its rules. ”To understand the game,” Poincaré wrote, ”is wholly another matter; it is to know why the player moves this piece rather than that oth...

Interpretability logic is a modal description of the interpretability predicate. The modal system IL is an extension of the provability logic GL (Gödel–Löb). Bisimulation quotients and largest bisimulations have been well studied for Kripke models. We examine interpretability logic and consider how these results extend to Veltman models. REPORTS ON MATHEMATICAL LOGIC 40 (2006), 59–73 Domagoj VR...

The paper presents a form of rendering classical mathematical notions by formal theories over suitable t-norm fuzzy logics in such a way that references to real numbers are eliminated from definitions and theorems, being removed to the standard semantics of fuzzy logic. Several examples demonstrate how this move conceptually simplifies the theory in exchange for non-classical reasoning, facilit...

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A spatial logic is a modal logic of which the models are the mathematical models of space. Successively considering the mathematical models of space that are the incidence geometry and the projective geometry, we will successively establish the language, the semanti-cal basis, the axiomatical presentation, the proof of the decidability and the proof of the completeness of INC, the modal multilo...

In this paper, we consider the development of a mathematical apparatus for logic programming of intelligent agents for searching, recognizing, collecting, and analyzing information on the Internet. The problem of ensuring soundness and completeness of logical inference in the dynamic environment of the Internet under the conditions of permanent update and revision of information is discussed. F...

Second-order logic has a number of attractive features, in particular the strong expressive resources it offers, and the possibility of articulating categorical mathematical theories (such as arithmetic and analysis). But it also has its costs. Five major charges have been launched against second-order logic: (1) It is not axiomatizable; as opposed to first-order logic, it is inherently incompl...

This study aims to develop a learning media product, namely the LoP Game improve Mathematical-Logic Learning Ability of Early Childhood Beginning. type research is Research and Development (R&D) using model developed by Borg Gall. There are 3 stages used in this from 10 proposed These include: information collecting, planning, preliminary form product. Data validity analysis was performed A...