This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieck’s view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers an...

This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieck’s view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers an...

Abstract While anti-exceptionalism about logic (AEL) is now a popular topic within the philosophy of logic, there’s still lack clarity over what proposal amounts to. currently, it most common to conceive AEL as that continuous with sciences . Yet, we show here, this conception unhelpful due both its precision, and distortion current debates. Rather, better understood rejection certain tradition...

We introduce an expansion of Basic Logic (BL) with new connectives which express fixed points of continuous formulas, i.e. formulas of BL whose connectives are among {&,∨,∧}. The algebraic semantics of this logic is studied together with some of its subclasses corresponding to extensions of the above-mentioned expansion. The axiomatic extensions are proved to be standard complete.

Fuzzy logics based on residuated t-norms provide a robust mathematical formalism for logical deduction under uncertain or vague premises. In this paper, we describe a decision algorithm for the tautology problem of Basic Logic, which is the logic of continuous t-norms and their residua [Háj98, CEGT00]. Our algorithm is a refinement of the semantic method of Baaz, Hájek, Montagna, and Veith [BHM...

Abstract. Logic-based methods provide a strategy for applying convex nonlinear programming to nonconvex global optimization. Such methods assume that the problem becomes convex when selected variables are fixed. The selected variables must be discrete, or else discretized if they are continuous. We provide a tutorial survey of disjunctive programming with convex relaxations, logic-based outer a...

This paper presents a symbolic model checking algorithm for continuous-time Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al 1]. The considered logic contains a time-bounded until-operator and a novel operator to express steady-state probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded unt...

Recently the question of standard completeness of MTL and its extensions were deeply studied. Jenei and Montagna showed that MTL logic satisfies standard completeness theorem (see [6]). In [2], the authors studied standard completeness of ΠMTL which is an axiomatic extension of MTL logic where the conjunction is interpreted by a left-continuous cancellative t-norm. They showed that ΠMTL logic i...

We generalise dynamic logic to a logic for differential-algebraic programs, i.e., discrete programs augmented with first-order differentialalgebraic formulas as continuous evolution constraints in addition to first-order discrete jump formulas. These programs characterise interacting discrete and continuous dynamics of hybrid systems elegantly and uniformly. For our logic, we introduce a calcul...

Dynamic Topological Logic provides a context for studying the confluence of the topological semantics for S4, based on topological spaces rather than Kripke frames; topological dynamics; and temporal logic. In the topological semantics for S4, 2 is interpreted as topological interior: thus S4 can be understood as the logic of topological spaces. Topological dynamics studies the asymptotic prope...