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52
Hyper Tableaux
, 1996
"... This paper introduces a variant of clausal normal form tableaux that we call "hyper tableaux". Hyper tableaux keep many desirable features of analytic tableaux while taking advantage of the central idea from (positive) hyper resolution, namely to resolve away all negative literals of a cla ..."
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Cited by 84 (20 self)
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clause in a single inference step. Another feature of the proposed calculus is the extensive use of universally quantified variables. This enables new efficient forwardchaining proof procedures for full first order theories as variants of tableaux calculi.
Developing Modal Tableaux and Resolution Methods via FirstOrder Resolution
"... abstract. This paper explores the development of calculi using different proof methods for propositional dynamic modal logics. Dynamic modal logics are PDLlike extended modal logics which are closely related to description logics. We show how tableau systems, modal resolution systems and RasiowaSi ..."
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Cited by 3 (2 self)
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Sikorski systems, which are dual tableau systems, can be developed and studied by using standard principles and methods of firstorder theorem proving. We translate modal logic reasoning problems to firstorder clausal form and then use a suitable refinement of resolution to construct and mimic derivations using
CRAIG INTERPOLATION FOR NETWORKS OF SENTENCES
, 2012
"... Abstract. The Craig Interpolation Theorem can be viewed as saying that in first order logic, two agents who can only communicate in their common language can cooperate in building proofs. We obtain generalizations of the Craig Interpolation Theorem for finite sets of agents with the following prope ..."
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Abstract. The Craig Interpolation Theorem can be viewed as saying that in first order logic, two agents who can only communicate in their common language can cooperate in building proofs. We obtain generalizations of the Craig Interpolation Theorem for finite sets of agents with the following
A Firstorder Simplification Rule with Constraints
 3RD INT. WORKSHOP ON FIRSTORDER THEOREM PROVING (FTP
, 2000
"... Several variants of a firstorder simplification rule for nonnormal form tableaux using syntactic constraints are presented. These can be used as a framework for porting refinements of clausal firstorder proof procedures to nonnormal form tableaux. Some experimental results obtained with a protot ..."
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Cited by 3 (3 self)
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Several variants of a firstorder simplification rule for nonnormal form tableaux using syntactic constraints are presented. These can be used as a framework for porting refinements of clausal firstorder proof procedures to nonnormal form tableaux. Some experimental results obtained with a
A Proof of Craig's Interpolation Theorem in Coq
"... INTRODUCTION 1 1 Introduction The aim of this project was to give a formal proof in type theory of some rst order syntactic theorems, as Craig's interpolation or cut elimination. As I knew neither Lego nor Coq, my rst work had been to learn one of them : James and Healfdene adviced me to learn ..."
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INTRODUCTION 1 1 Introduction The aim of this project was to give a formal proof in type theory of some rst order syntactic theorems, as Craig's interpolation or cut elimination. As I knew neither Lego nor Coq, my rst work had been to learn one of them : James and Healfdene adviced me
Efficient Generation of Craig Interpolants in Satisfiability Modulo Theories
"... The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of firstorder logic, which are amenable for effective decision procedures, called Satisfiability Modulo The ..."
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Cited by 19 (6 self)
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The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of firstorder logic, which are amenable for effective decision procedures, called Satisfiability Modulo
Ordered Tableaux: Extensions and Applications
 Proc. International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, PontMousson
, 1997
"... . In this paper several conceptual extensions to the theory of orderrestricted free variable clausal tableaux which was initiated in [9, 8] are presented: atom orderings are replaced by the more general concept of a selection function, the substitutivity condition required for lifting is for certai ..."
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Cited by 6 (3 self)
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. In this paper several conceptual extensions to the theory of orderrestricted free variable clausal tableaux which was initiated in [9, 8] are presented: atom orderings are replaced by the more general concept of a selection function, the substitutivity condition required for lifting
Debugging Axioms with HyperTableaux
, 1998
"... 3), if the automated theorem prover does not terminate within ressource bounds. Therefore, I propose an approach that inspects partial proofs achieved with a hypertableaux theorem prover and enables the detection of deficient axioms. 2 Theorem Proving with HyperTableaux Hypertableaux constitut ..."
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constitute a complete, modelgenerating clausal tableaux calculus for firstorder logic and have been introduced by [3], although an earlier, more restricted version is used in the theorem provers SATCHMO [7] and MGTP [5]. Hypertableaux combine analytical reasoning inherited from tableaux calculi
Craig’s interpolation theorem formalised and mechanised
 in Isabelle/HOL. Logic in Computer Science
, 2006
"... We formalise and mechanise a construtive, proof theoretic proof of Craig’s Interpolation Theorem in Isabelle/HOL. We give all the definitions and lemma statements both formally and informally. We also transcribe informally the formal proofs. We detail the main features of our mechanisation, such as ..."
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Cited by 4 (0 self)
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, such as the formalisation of binding for first order formulae. We also give some applications of Craig’s Interpolation Theorem. 1.
The Craig interpolation theorem in abstract model theory
"... Abstract The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will model theory for identifying “natural, ” robust extensions of first order logic. My argument is supported by the observation that logics wh ..."
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Cited by 2 (1 self)
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Abstract The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will model theory for identifying “natural, ” robust extensions of first order logic. My argument is supported by the observation that logics
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