Related papers: Representation Theorems for Cumulative Proposition…
One advantage of paraconsistent logic is that it can deal with inconsistencies without making the system trivial. However, unlike classical propositional calculus, its deductive system is limited, and the meaning of paraconsistent negation…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
This paper is part of a project that is based on the notion of dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In previous work, we investigated the expressive and computational power of…
We construct a weak dilation of a not necessarily unital CP-semigroup to an E-semigroup acting on the adjointable operators of a Hilbert module with a unit vector. We construct the dilation in such a way that the dilating E-semigroup has a…
We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
Dynamic epistemic logics which model abilities of agents to make various announcements and influence each other's knowledge have been studied extensively in recent years. Two notable examples of such logics are Group Announcement Logic and…
We extend the treatment of functional dependence, the basic concept of dependence logic, to include the possibility of dependence with a limited number of exceptions. We call this approximate dependence. The main result of the paper is a…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
Given a category C of a combinatorial nature, we study the following fundamental question: how does the combinatorial behavior of C affect the algebraic behavior of representations of C? We prove two general results. The first gives a…
We introduce a graph-theoretical representation of proofs of multiplicative linear logic which yields both a denotational semantics and a notion of truth. For this, we use a locative approach (in the sense of ludics) related to game…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
A semantic tableau method, called an argumentation tableau, that enables the derivation of arguments, is proposed. First, the derivation of arguments for standard propositional and predicate logic is addressed. Next, an extension that…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…
Given a class C of word languages, the C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the…
A representation theorem relates different mathematical structures by providing an isomorphism between them: that is, a one-to-one correspondence preserving their original properties. Establishing that the two structures substantially…
With this chapter we provide a compact yet complete survey of two most remarkable "representation theorems": every arguesian projective geometry is represented by an essentially unique vector space, and every arguesian Hilbert geometry is…
The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to…