相关论文: Deducibility Theorems in Boolean Logic

Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…

We give a presentation of Krivine and Parigot's Second-order functional arithmetic in Deduction modulo. Expressing this theory in Deduction modulo sheds light on an original aspect of this theory: the fact that programs are specified, not…

In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\Box$ and $\triangle$ that…

We study an extension of \g propositional logic whose corresponding algebra is an ordered Abelian group. Then we expand the ideas to first-order case of this logic.

The decidability of a logical system refers to the existence of an algorithm that can determine whether any given formula in that system is a theorem. In this paper, Harrop's lemma is used to prove the decidability of quantum modal logic.

In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.

Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…

We introduce ologisms. They generate from ologs by extending their logical expressivity, from the possibility of considering constraints of equational nature only to the possibility of considering constraints of syllogistic nature, in…

Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional…

Here, in a series of articles, we show methods for calculating propositional statements using algebraic polynomials as symbols for the connectives, which are named operators. These polynomials originate from the transformation between the…

A prototype system is described whose core functionality is, based on propositional logic, the elimination of second-order operators, such as Boolean quantifiers and operators for projection, forgetting and circumscription. This approach…

In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…

Two results are presented concerning the entailment problem in Separation Logic with inductively defined predicate symbols and theory reasoning. First, we show that the entailment problem is undecidable for rules with bounded tree-width, if…

Goedel's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by Goedel to…

In this paper, general logic-systems and a necessary and sufficient algorithm are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a…

Starting with the deontic principles in M\={\i}m\=a\d{m}s\=a texts we introduce a new deontic logic. We use general proof-theoretic methods to obtain a cut-free sequent calculus for this logic, resulting in decidability, complexity results…

Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…

This work presents an operational and geometric approach to logic. It starts from the multilinear elective decomposition of binary logical functions in the original form introduced by George Boole. A justification on historical grounds is…

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…

Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…