Related papers: On prevarieties of logic
We prove that there are continuum-many axiomatic extensions of the full Lambek calculus with exchange that have the deductive interpolation property. Further, we extend this result to both classical and intuitionistic linear logic as well…
The paper studies hereditarily complete superintuitionistic deductive systems, that is, the deductive system which logic is an extension of the intuitionistic propositional logic. It is proven that for deductive systems a criterion of…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
To provide a categorical semantics for co-intuitionistic logic one has to face the fact, noted by Tristan Crolard, that the definition of co-exponents as adjuncts of coproducts does not work in the category Set, where coproducts are…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…
In this paper we prove that three of the main propositional logics of dependence (including propositional dependence logic and inquisitive logic), none of which is structural, are structurally complete with respect to a class of…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
We prove completeness of preferential conditional logic with respect to convexity over finite sets of points in the Euclidean plane. A conditional is defined to be true in a finite set of points if all extreme points of the set interpreting…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
In the present paper, we propose Abstract Algebraic Logic (AAL) as a general logical framework for Judgment Aggregation. Our main contribution is a generalization of Herzberg's algebraic approach to characterization results in on judgment…
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…
We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…
We study geometric representation theory of Lie algebroids. A new equivalence relation for integrable Lie algebroids is introduced and investigated. It is shown that two equivalent Lie algebroids have equivalent categories of infinitesimal…
Let C subset Reg be a non-empty class (of regular cardinal). Then the logic L(Q^{cf}_C) has additional nice properties: it has homogeneous model existence property.
In this paper we consider, from a computational point of view, the problem of classifying logics within the Leibniz and Frege hierarchies typical of abstract algebraic logic. The main result states that, for logics presented syntactically,…
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.
In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…