Hybrid Deduction-Refutation Systems for FDE-Based Logics

Hybrid deduction-refuation systems are presented for four first-degree entailment based logics. The hybrid systems are shown to be deductively and refutationally sound with respect to their logics. The proofs of completeness are presented in a uniform way. The paper builds on work by Goranko, who presented a deductively and refutationally sound and complete hybrid system for classical logic

Hybrid Deduction-Refutation Systems for FDE-Based Logics

Hybrid deduction-refuation systems are presented for four first-degree entailment based logics. The hybrid systems are shown to be deductively and refutationally sound with respect to their logics. The proofs of completeness are presented in a uniform way. The paper builds on work by Goranko, who presented a deductively and refutationally sound and complete hybrid system for classical logic

Deductive Systems in Traditional and Modern Logic

The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic

A resolution principle for clauses with constraints

We introduce a general scheme for handling clauses whose variables are constrained by an underlying constraint theory. In general, constraints can be seen as quantifier restrictions as they filter out the values that can be assigned to the variables of a clause (or an arbitrary formulae with restricted universal or existential quantifier) in any of the models of the constraint theory. We present a resolution principle for clauses with constraints, where unification is replaced by testing constraints for satisfiability over the constraint theory. We show that this constrained resolution is sound and complete in that a set of clauses with constraints is unsatisfiable over the constraint theory if we can deduce a constrained empty clause for each model of the constraint theory, such that the empty clauses constraint is satisfiable in that model. We show also that we cannot require a better result in general, but we discuss certain tractable cases, where we need at most finitely many such empty clauses or even better only one of them as it is known in classical resolution, sorted resolution or resolution with theory unification

Scavenger 0.1: A Theorem Prover Based on Conflict Resolution

This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a first-order generalization of) unit propagation as well as a rule for assuming decision literals and a rule for deriving new clauses by (a first-order generalization of) conflict-driven clause learning.Comment: Published at CADE 201

Refutation Systems : An Overview and Some Applications to Philosophical Logics

Refutation systems are systems of formal, syntactic derivations, designed to derive the non-valid formulas or logical consequences of a given logic. Here we provide an overview with comprehensive references on the historical development of the theory of refutation systems and discuss some of their applications to philosophical logics

Preprints of Proceedings of GWAI-92

This is a preprint of the proceedings of the German Workshop on Artificial Intelligence (GWAI) 1992. The final version will appear in the Lecture Notes in Artificial Intelligence