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27
'One is a Lonely Number': on the logic of communication
, 2002
"... Logic is not just about singleagent notions like reasoning, or zeroagent notions like truth, but also about communication between two or more people. What we tell and ask each other can be just as 'logical' as what we infer in Olympic solitude. We show how such interactive phenomena can ..."
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Cited by 61 (15 self)
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Logic is not just about singleagent notions like reasoning, or zeroagent notions like truth, but also about communication between two or more people. What we tell and ask each other can be just as 'logical' as what we infer in Olympic solitude. We show how such interactive phenomena can be studied systematically by merging epistemic and dynamic logic.
Monodic fragments of firstorder temporal logics: 20002001 A.D.
"... The aim of this paper is to summarize and analyze some results obtained in 20002001 about decidable and undecidable fragments of various firstorder temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the `temporal community&a ..."
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Cited by 48 (8 self)
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The aim of this paper is to summarize and analyze some results obtained in 20002001 about decidable and undecidable fragments of various firstorder temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the `temporal community' to a number of interesting open problems.
The TwoVariable Guarded Fragment with Transitive Relations
 In Proc. LICS'99
, 1999
"... We consider the restriction of the guarded fragment to the twovariable case where, in addition, binary relations may be specified as transitive. We show that (i) this very restricted form of the guarded fragment without equality is undecidable and that (ii) when allowing nonunary relations to occu ..."
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Cited by 34 (1 self)
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We consider the restriction of the guarded fragment to the twovariable case where, in addition, binary relations may be specified as transitive. We show that (i) this very restricted form of the guarded fragment without equality is undecidable and that (ii) when allowing nonunary relations to occur only in guards, the logic becomes decidable. The latter subclass of the guarded fragment is the one that occurs naturally when translating multimodal logics of the type K4, S4 or S5 into rstorder logic. We also show that the loosely guarded fragment without equality and with a single transitive relation is undecidable.
Complexity of Modal Logics of Relations
, 1997
"... We consider two families of modal logics of relations: arrow logic and cylindric modal logic and several natural expansions of these, interpreted on a range of (relativised) modelclasses. We give a systematic study of the complexity of the validity problem of these logics, obtaining price tags for ..."
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Cited by 24 (9 self)
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We consider two families of modal logics of relations: arrow logic and cylindric modal logic and several natural expansions of these, interpreted on a range of (relativised) modelclasses. We give a systematic study of the complexity of the validity problem of these logics, obtaining price tags for various features as assumptions on the universe of the models, similarity types, and number of variables involved. The general picture is that the process of relativisation turns an undecidable logic into one whose validity problem is exptimecomplete. There are interesting deviations to this though, which we also discuss. The numerous results in this paper are all directed to obtain a better understanding why relativisation can turn an undecidable modal logic of relations into a decidable one. We connect the semantic way of "taming logic" by relativisation with the syntactic approach of isolating decidable socalled guarded fragments by showing that validity of loosely guarded formulas is p...
Guarded open answer set programming
 LPNMR
, 2005
"... Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program’s constants. We define a fixed point logic (FPL) extension of Clark’s completion such that open answer sets correspond to models of FPL formulas and ..."
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Cited by 23 (7 self)
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Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program’s constants. We define a fixed point logic (FPL) extension of Clark’s completion such that open answer sets correspond to models of FPL formulas and identify a syntactic subclass of programs, called (loosely) guarded programs. Whereas reasoning with general programs in OASP is undecidable, the FPL translation of (loosely) guarded programs falls in the decidable (loosely) guarded fixed point logic (µ(L)GF). Moreover, we reduce normal closed ASP to loosely guarded OASP, enabling a characterization of an answer set semantics by µLGF formulas. Finally, we relate guarded OASP to Datalog LITE, thus linking an answer set semantics to a semantics based on fixed point models of extended stratified Datalog programs. From this correspondence, we deduce 2EXPTIMEcompleteness of satisfiability checking w.r.t. (loosely) guarded programs.
Tractable and Decidable Fragments of Conceptual Graphs
 IN PROCEEDINGS OF ICCS'99
, 1999
"... It is wellknown that problems like validity and subsumption of general CGs are undecidable, whereas subsumption is NPcomplete for simple conceptual graphs (SGs) and tractable for SGs that are trees. We will employ results on decidable fragments of rstorder logic to identify a natural and expressi ..."
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Cited by 15 (0 self)
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It is wellknown that problems like validity and subsumption of general CGs are undecidable, whereas subsumption is NPcomplete for simple conceptual graphs (SGs) and tractable for SGs that are trees. We will employ results on decidable fragments of rstorder logic to identify a natural and expressive fragment of CGs for which validity and subsumption is decidable in ExpTime. In addition, we will extend existing work on the connection between SGs and description logics (DLs) by identifying a DL that corresponds to the class of SGs that are trees. This yields a tractability result previously unknown in the DL community.
Modal Logic: A Semantic Perspective
 ETHICS
, 1988
"... This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimul ..."
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Cited by 12 (2 self)
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This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimulations) which underly it. We introduce the syntax and semantics of basic modal logic, discuss its expressivity at the level of models, examine its computational properties, and then consider what it can say at the level of frames. We then move beyond the basic modal language, examine the kinds of expressivity offered by a number of richer modal logics, and try to pin down what it is that makes them all ‘modal’. We conclude by discussing an example which brings many of the ideas we discuss into play: games.
A Survey of Decidable FirstOrder Fragments and Description Logics
 Journal of Relational Methods in Computer Science
, 2004
"... The guarded fragment and its extensions and subfragments are often considered as a framework for investigating the properties of description logics. There are also other, some less wellknown, decidable fragments of firstorder logic which all have in common that they generalise the standard tran ..."
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Cited by 10 (2 self)
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The guarded fragment and its extensions and subfragments are often considered as a framework for investigating the properties of description logics. There are also other, some less wellknown, decidable fragments of firstorder logic which all have in common that they generalise the standard translation of to firstorder logic. We provide a short survey of some of these fragments and motivate why they are interesting with respect to description logics, mentioning also connections to other nonclassical logics.
Finite conformal hypergraph covers and Gaifman cliques in finite structures
 Bull. Symbolic Logic
, 2002
"... We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid al ..."
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Cited by 10 (6 self)
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We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques – thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms of relational structures, we show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications answers an open question about a clique constrained strengthening of the extension property for partial automorphisms (EPPA) of Hrushovski, Herwig and Lascar. A second application provides an alternative proof of the finite model property (FMP) for the clique guarded fragment of firstorder logic CGF, by reducing (finite) satisfiability in CGF to (finite) satisfiability in the guarded fragment, GF.
Towards a Diagrammatic Reasoning System for Description Logics
, 2006
"... Diagrammatic reasoning is a tradition of visual logic that allows sentences that are equivalent to first order logic to be written in a visual or structural form: typically for improved usability. A calculus for the diagram is then defined that allows wellformed formulas to be derived. This calculu ..."
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Cited by 9 (2 self)
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Diagrammatic reasoning is a tradition of visual logic that allows sentences that are equivalent to first order logic to be written in a visual or structural form: typically for improved usability. A calculus for the diagram is then defined that allows wellformed formulas to be derived. This calculus is intended to simulate logical inference. Description logics (DLs) have become a popular subset of first order logic that have decidable tableau theorem provers and are sound and complete. Our paper explores whether several existing wellknown diagrammatic reasoning systems are compatible with DLs. We provide translations between the DL ALCI and a appropriate subset of Peirce’s relation graphs, termed RG ALCI. A precise formal elaboration, where relation graphs are for example defined in terms of mathematical graph theory, goes beyond the scope of this paper. We will provide a semiformal approach instead.