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70
Spider diagrams
"... The use of diagrams in mathematics has traditionally been restricted to guiding intuition and communication. With rare exceptions such as Peirce’s α and β systems, purely diagrammatic formal reasoning has not been in the mathematicians or logicians toolkit. This paper develops a purely diagrammatic ..."
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Cited by 75 (31 self)
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The use of diagrams in mathematics has traditionally been restricted to guiding intuition and communication. With rare exceptions such as Peirce’s α and β systems, purely diagrammatic formal reasoning has not been in the mathematicians or logicians toolkit. This paper develops a purely diagrammatic reasoning system of ‘spider diagrams ’ that builds on Euler, Venn and Peirce diagrams. The system is known to be expressively equivalent to first order monadic logic with equality. We develop two levels of diagrammatic syntax: an ‘abstract ’ syntax that captures the structure of diagrams and a ‘concrete’ syntax that captures topological properties of drawn diagrams. A number of simple diagrammatic transformation rules are given and the resulting reasoning system is shown to be sound and complete. 1
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 72 (17 self)
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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 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.
Answer Sets for Consistent Query Answering in Inconsistent Databases
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2003
"... A relational database is inconsistent if it does not satisfy a given set of integrity constraints. Nevertheless, it is likely that most of the data in it is consistent with the constraints. In this paper we apply logic programming based on answer sets to the problem of retrieving consistent informat ..."
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Cited by 39 (8 self)
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A relational database is inconsistent if it does not satisfy a given set of integrity constraints. Nevertheless, it is likely that most of the data in it is consistent with the constraints. In this paper we apply logic programming based on answer sets to the problem of retrieving consistent information from a possibly inconsistent database. Since consistent information persists from the original database to every of its minimal repairs, the approach is based on a specification of database repairs using disjunctive logic programs with exceptions, whose answer set semantics can be represented and computed by systems that implement stable model semantics. These programs allow us to declare persistence by default of data from the original instance to the repairs; and changes to restore consistency, by exceptions. We concentrate mainly on logic programs for binary integrity constraints, among which we find most of the integrity constraints found in practice.
A FirstOrder Logic DavisPutnamLogemannLoveland Procedure
"... The DavisPutnamLogemannLoveland procedure (DPLL) was introduced in the early ..."
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Cited by 38 (6 self)
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The DavisPutnamLogemannLoveland procedure (DPLL) was introduced in the early
Hybrid Logics
"... This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur ..."
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Cited by 36 (10 self)
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This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur
GentzenType Systems, Resolution And Tableaux
 Journal of Automated Reasoning
, 1993
"... Introduction In advanced books and courses on logic (e.g. [Sm], [BM]) Gentzentype systems or their dual, tableaux, are described as techniques for showing validity of formulae which are more practical than the usual Hilberttype formalisms. People who have learnt these methods often wonder why the ..."
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Cited by 32 (12 self)
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Introduction In advanced books and courses on logic (e.g. [Sm], [BM]) Gentzentype systems or their dual, tableaux, are described as techniques for showing validity of formulae which are more practical than the usual Hilberttype formalisms. People who have learnt these methods often wonder why the Automated Reasoning community seems to ignore them and prefers instead the resolution method. Some of the classical books on AD (such as [CL], [Lo]) do not mention these methods at all. Others (such as [Ro]) do, but the connections and reasons for preference remain unclear after reading them (at least to the present author, and obviously also the authors of [OS], in which a theoremprover, based exclusively on tableaux, is described). The confusion becomes greater when the reader is introduced to Kowalski's form of a clause ([Ko], [Bu]), which is nothing but a Gentzen's sequent of atomic formulae, and when he realizes that resolution is just a form of a Cut, and so that while the<F1
Embedding NonGround Logic Programs into Autoepistemic Logic for Knowledge Base Combination
, 2008
"... ..."
Simplification  A general constraint propagation technique for propositional and modal tableaux
, 1998
"... . Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than DavisPutnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle ..."
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Cited by 24 (2 self)
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. Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than DavisPutnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle (viz. the cutrule) but there is another source of inefficiency: the lack of constraint propagation mechanisms. This paper proposes an innovation in this direction: the rule of simplification, which plays for tableaux the role of subsumption for resolution and of unit for the DavisPutnam procedure. The simplicity and generality of simplification make possible its extension in a uniform way from propositional logic to a wide range of modal logics. This technique gives an unifying view of a number of tableauxlike calculi such as DPLL, KE, HARP, hypertableaux, BCP, KSAT. We show its practical impact with experimental results for random 3SAT and the industrial IFIP benchmarks for hardware ve...
First Order Abduction Via Tableau and Sequent Calculi
 Bulletin of the IGPL
, 1993
"... The formalization of abductive reasoning is still an open question: there is no general agreement on the boundary of some basic concepts, such as preference criteria for explanations, and the extension to first order logic has not been settled. Investigating the nature of abduction outside the conte ..."
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Cited by 22 (6 self)
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The formalization of abductive reasoning is still an open question: there is no general agreement on the boundary of some basic concepts, such as preference criteria for explanations, and the extension to first order logic has not been settled. Investigating the nature of abduction outside the context of resolution based logic programming still deserves attention, in order to characterize abductive explanations without tailoring them to any fixed method of computation. In fact, resolution is surely not the best tool for facing metalogical and prooftheoretical questions. In this work the analysis of the concepts involved in abductive reasoning is based on analytical proof systems, i.e. tableaux and Gentzentype systems. A proof theoretical abduction method for first order classical logic is defined, based on the sequent calculus and a dual one, based on semantic tableaux. The methods are sound and complete and work for full first order logic, without requiring any preliminary reductio...
A Model Elimination Calculus with Builtin Theories
 Proceedings of the 16th German AIConference (GWAI92
, 1992
"... this paper, we will show how to extend model elimination with theory reasoning. Technically, theory reasoning means to relieve a calculus from explicit reasoning in some domain (e.g. equality, partial orders) by taking apart the domain knowledge and treating it by special inference rules. In an impl ..."
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Cited by 17 (10 self)
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this paper, we will show how to extend model elimination with theory reasoning. Technically, theory reasoning means to relieve a calculus from explicit reasoning in some domain (e.g. equality, partial orders) by taking apart the domain knowledge and treating it by special inference rules. In an implementation, this results in a universal "foreground" reasoner that calls a specialized "background" reasoner for theory reasoning. Theory reasoning comes in two variants (Sti85) : total and