199 research outputs found
Generating Schemata of Resolution Proofs
Two distinct algorithms are presented to extract (schemata of) resolution
proofs from closed tableaux for propositional schemata. The first one handles
the most efficient version of the tableau calculus but generates very complex
derivations (denoted by rather elaborate rewrite systems). The second one has
the advantage that much simpler systems can be obtained, however the considered
proof procedure is less efficient
The Universe of Approximations
AbstractThe idea of approximate entailment has been in [13] as a way of modeling the reasoning of an agent with limited resources. They proposed a system in which a family of logics, parameterized by a set of propositional letters, approximates classical logic as the size of the set increases.In this paper, we take the idea further, extending two of their systems to deal with full propositional logic, giving them semantics and sound and complete proof methods based on tableaux. We then present a more general system of which the two previous systems are particular cases and show how it can be used to formalize heuristics used in theorem proving
Range-Restricted Interpolation through Clausal Tableaux
We show how variations of range-restriction and also the Horn property can be
passed from inputs to outputs of Craig interpolation in first-order logic. The
proof system is clausal tableaux, which stems from first-order ATP. Our results
are induced by a restriction of the clausal tableau structure, which can be
achieved in general by a proof transformation, also if the source proof is by
resolution/paramodulation. Primarily addressed applications are query synthesis
and reformulation with interpolation. Our methodical approach combines
operations on proof structures with the immediate perspective of feasible
implementation through incorporating highly optimized first-order provers
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
The complexity of theorem proving in circumscription and minimal entailment
We provide the first comprehensive proof-complexity analysis of different proof systems for propositional circumscription. In particular, we investigate two sequent-style calculi: MLK defined by Olivetti [28] and CIRC introduced by Bonatti and Olivetti [8], and the tableaux calculus NTAB suggested by Niemelä [26]. In our analysis we obtain exponential lower bounds for the proof size in NTAB and CIRC and show a polynomial simulation of CIRC by MLK. This yields a chain NTAB < CIRC < MLK of proof systems for circumscription of strictly increasing strength with respect to lengths of proofs
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