Deduction chains represent a syntactic and in a certain sense constructive method for proving completeness of a formal system. Given a formula φ, the deduction chains of φ are built up by systematically decomposing φ into its subformulae. In the case where φ is a valid formula, the decomposition yields a (usually cut-free) proof of φ. If φ is not valid, the decomposition produces a countermodel...

Appeared in: N.V. Murray, editor, Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX’99), Lecture Notes in Artificial Intelligence 1617, Springer, pages 247–262, 1999. We present a tableau calculus for reasoning in fragments of natural language. We focus on the problem of pronoun resolution and the way in which it complicates automated theorem proving for natural language ...

We prove in HOL that three proof systems for classical rst-order predicate logic, the Hilbertian axiomatization, the system of natural deduction, and a variant of sequent calculus, are isomorphic. The isomorphism is in the sense that provability of a conclusion from hypotheses in one of these proof systems is equivalent to provability of this conclusion from the same hypotheses in the others. P...

Birkhoff (quasi-)variety categorical axiomatizability results have fascinated many scientists by their elegance, simplicity and generality. The key factor leading to their generality is that equations, conditional or not, can be regarded as special morphisms or arrows in a special category, where their satisfaction becomes injectivity, a simple and abstract categorical concept. A natural and ch...

We introduce an encoding of the set theory of the B method using polymorphic types and deduction modulo, which is used for the automated verification of proof obligations in the framework of the BWare project. Deduction modulo is an extension of predicate calculus with rewriting both on terms and propositions. It is well suited for proof search in theories because it turns many axioms into rewr...

The so called cogen approach to program specialisation writing a compiler generator instead of a specialiser has been used with considerable success in partial evaluation of both functional and imperative languages This paper demonstrates that this approach is also applicable to partial evaluation of logic programming languages also called partial deduction Self application has not been as much...

Superdeduction is a formalism closely related to deduction modulo which permits to enrich a first-order deduction system—such as natural deduction or sequent calculus— with new inference rules automatically computed from the presentation of a theory. We give a natural encoding from every Pure Type System (PTS) into superdeduction by defining an appropriate first-order theory. We prove that this...

We present a new approach to probabilistic logic programs with a possible worlds semantics. Classical program clauses are extended by a subinterval of [0; 1] that describes the range for the conditional probability of the head of a clause given its body. We show that deduction in the defined probabilistic logic programs is computationally more complex than deduction in classical logic programs....

The logic of abduction and deduction contribute to our conceptual understanding of a phenomenon, while the logic of induction adds quantitative details to our conceptual knowledge. In this paper, we will look into how this reasoning techniquesabduction, deduction and induction, are relevant in neural networks logic programming. Deduction simplifies the knowledge representation without affecting...

In this paper we ask the question whether the extended Frege proof system EF satisfies a weak version of the deduction theorem. We prove that if this is the case, then complete disjoint NP-pairs exist. On the other hand, if EF is an optimal proof system, then the weak deduction theorem holds for EF . Hence the weak deduction property for EF is a natural intermediate condition between the optima...