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Logics of Formal Inconsistency
 Handbook of Philosophical Logic
"... 1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory ..."
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1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory
Hybrid Tableaux for the Difference Modality
, 2008
"... We present the first tableaubased decision procedure for basic hybrid logic with the difference modality. The decision procedure is gracefully degrading in that the less expressive constructs don’t pay for the computationally expensive difference modality. The procedure can be specialized to reflex ..."
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We present the first tableaubased decision procedure for basic hybrid logic with the difference modality. The decision procedure is gracefully degrading in that the less expressive constructs don’t pay for the computationally expensive difference modality. The procedure can be specialized to reflexive and transitive frames. Key features of our approach are nominal elimination, patternbased blocking, and expansion control.
BDDs and Automated Deduction
"... BDDs (binary decision diagrams) are a very succesful tool for handling boolean functions, but one which has not yet attracted the attention of many automated deduction specialists. We give an overview of BDDs from an automated deduction perspective, showing what can be done with them in propositiona ..."
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BDDs (binary decision diagrams) are a very succesful tool for handling boolean functions, but one which has not yet attracted the attention of many automated deduction specialists. We give an overview of BDDs from an automated deduction perspective, showing what can be done with them in propositional and firstorder logic, and discuss the parallels to wellknown methods like tableaux and resolution.
D.: Equal Rights for the Cut: Computable Nonanalytic Cuts in Cutbased Proofs
 Logic Journal of the IGPL
, 2007
"... This work studies the structure of proofs containing nonanalytic cuts in the cutbased system, a sequent inference system in which the cut rule is not eliminable and the only branching rule is the cut. Such sequent system is invertible, leading to the KEtableau decision method. We study the struct ..."
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This work studies the structure of proofs containing nonanalytic cuts in the cutbased system, a sequent inference system in which the cut rule is not eliminable and the only branching rule is the cut. Such sequent system is invertible, leading to the KEtableau decision method. We study the structure of such proofs, proving the existence of a normal form for them in the form of a combtree proof. We then concentrate on the problem of efficiently computing nonanalytic cuts. For that, we study the generalisation of techniques present in many modern theorem provers, namely the techniques of conflictdriven formula learning.
Automated Deduction with Shannon Graphs
 Journal of Logic and Computation. In
, 1995
"... Binary Decision Diagrams (BDDs) are a wellknown tool for representing Boolean functions. We show how BDDs can be extended to full firstorder logic by integrating means for representing quantifiers. The resulting structures are called Shannon graphs. A calculus based on these Shannon graphs is set ..."
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Binary Decision Diagrams (BDDs) are a wellknown tool for representing Boolean functions. We show how BDDs can be extended to full firstorder logic by integrating means for representing quantifiers. The resulting structures are called Shannon graphs. A calculus based on these Shannon graphs is set up, and its soundness and completeness proofs are outlined. A comparison of deduction with firstorder BDDs and semantic tableaux shows that both calculi are closely related. From a practical perspective, however, BDDs have advantages over tableaux: they provide a more compact representation, since BDDs can be understood as a linear, graphical representation of a fully expanded tableaux. Furthermore, BDDs represent not only the models of a formula, but also its counter models: this offers a very efficient way to represent lemmata during the proof search. The last part of the paper introduces a compilationbased approach to implementing deduction systems based on Shannon graphs. The idea is t...
A Contextbased Logic for Distributed Knowledge Representation and Reasoning
 Modelling and Using Context
, 1999
"... This paper is concerned with providing a logic, called Distributed First Order Logic (DFOL), for the formalization of distributed knowledge representation and reasoning systems. In such systems knowledge is contained in a set of heterogeneous subsystems. Each subsystem represents, using a possibly d ..."
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This paper is concerned with providing a logic, called Distributed First Order Logic (DFOL), for the formalization of distributed knowledge representation and reasoning systems. In such systems knowledge is contained in a set of heterogeneous subsystems. Each subsystem represents, using a possibly different language, partial knowledge about a subset of the whole domain, it is able to reason about such a knowledge, and it is able to exchange knowledge with other subsystems via query answering. Our approach is to represent each subsystem as a context, each context having its own language, a set of basic facts describing what is "explicitly known" by the subsystem, and a set of inference rules representing the reasoning capabilities of the subsystem. Knowledge exchange is represented by two different relations on contexts: the former on the languages (query mapping) and the latter on the domains (answer mapping) of different contexts. DFOL is based on a semantics for contextua...
Accelerating Tableaux Proofs using Compact Representations
, 1993
"... In this article a modified form of tableau calculus, called Tableau Graph Calculus, is presented for overcoming the wellknown inefficiencies of the traditional tableau calculus to a large extent. This calculus is based on a compact representation of analytic tableaux by using graph structures calle ..."
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In this article a modified form of tableau calculus, called Tableau Graph Calculus, is presented for overcoming the wellknown inefficiencies of the traditional tableau calculus to a large extent. This calculus is based on a compact representation of analytic tableaux by using graph structures called tableau graphs. These graphs are obtained from the input formula in linear time and incorporate most of the rule applications of normal tableau calculus during the conversion process. The size of this representation is linear with respect to the length of the input formula and the graph closely resembles the proof tree of tableau calculi thus retaining the naturalness of the proof procedure. As a result of this preprocessing step, tableau graph calculus has only a single rule which is repeatedly applied to obtain a proof. Many optimizations for the applications of this rule, to effectively prune the search space, are presented as well. Brief details of an implemented prover called FAUST, e...
Translating Linear Temporal Logic to Deterministic ωAutomata
 GI/ITG/GMM WORKSHOP METHODEN DES ENTWURFS UND DER VERIFIKATION DIGITALER SYSTEME
, 1997
"... In this paper, a new algorithm for translating linear time temporal logic (LTL) into deterministic ωautomata is presented which circumvents the usual tableau construction. The algorithm is not limited to a special kind of ωautomaton. As most decidability problems for ωautomata can be reduced to c ..."
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In this paper, a new algorithm for translating linear time temporal logic (LTL) into deterministic ωautomata is presented which circumvents the usual tableau construction. The algorithm is not limited to a special kind of ωautomaton. As most decidability problems for ωautomata can be reduced to corresponding CTL model checking problems, the presented algorithm can be used to translate LTL problems into equivalent CTL model checking problems. As a consequence, the translation method allows the use of symbolic traversal methods based on BDDs for LTL theorem proving as well as for LTL model checking.