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14
Internalizing Labelled Deduction
 Journal of Logic and Computation
, 2000
"... This paper shows how to internalize the Kripke satisfaction denition using the basic hybrid language, and explores the proof theoretic consequences of doing so. As we shall see, the basic hybrid language enables us to transfer classic Gabbaystyle labelled deduction methods from the metalanguage to ..."
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Cited by 79 (21 self)
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This paper shows how to internalize the Kripke satisfaction denition using the basic hybrid language, and explores the proof theoretic consequences of doing so. As we shall see, the basic hybrid language enables us to transfer classic Gabbaystyle labelled deduction methods from the metalanguage to the object language, and to handle labelling discipline logically. This internalized approach to labelled deduction links neatly with the Gabbaystyle rules now widely used in modal Hilbertsystems, enables completeness results for a wide range of rstorder denable frame classes to be obtained automatically, and extends to many richer languages. The paper discusses related work by Jerry Seligman and Miroslava Tzakova and concludes with some reections on the status of labelling in modal logic. 1 Introduction Modern modal logic revolves around the Kripke satisfaction relation: M;w ': This says that the model M satises (or forces, or supports) the modal formula ' at the state w in M....
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 60 (18 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
A Modal Perspective on the Computational Complexity of Attribute Value Grammar
, 1992
"... Many of the formalisms; used in Attribute Value grammar are notational variants of languages of propositional modal logic,. and testing whether two Attribute Value descriptions unify amounts to testing for modal satisfiability. In this paper we put this. observation to work. We study the complexit ..."
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Cited by 48 (7 self)
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Many of the formalisms; used in Attribute Value grammar are notational variants of languages of propositional modal logic,. and testing whether two Attribute Value descriptions unify amounts to testing for modal satisfiability. In this paper we put this. observation to work. We study the complexity of the satisfiability problem for nine modal languages which mirror different aspects of AVS description formalisms, including the ability to express reeintrancy, the ability to express generalisations, and the ability to express recursive constraints. Two mail techniques axe used: either Kripke models with desirable properties are constructed, or modalities are used to simulate fragments of Propositional Dynamic Logic. Further possibilities for the application of modal logic in computational linguistics are noted
A Modal Perspective on Path Constraints
, 2003
"... We analyze several classes of path constraints for semistructured data and prove a umber of decidability and complexity results for such constraints. While some of our decidability results were known before, we believe that our improved complexity bounds are new. Our proofs are based on technique ..."
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Cited by 33 (0 self)
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We analyze several classes of path constraints for semistructured data and prove a umber of decidability and complexity results for such constraints. While some of our decidability results were known before, we believe that our improved complexity bounds are new. Our proofs are based on techniques from modal logic and automata theory. We believe that our modal logic perspective sheds additional light on the reasons for previously known decidability and complexity results.
Structures, Languages and Translations: the Structural Approach to Feature Logic
 Constraints, Language and Computation
, 1994
"... This paper discusses an approach to feature logic called the structural approach. The method consists in first viewing feature structures as models (or relational structures) in the standard model theoretic sense, and then going on to consider various languages that can be interpeted on these struct ..."
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Cited by 17 (2 self)
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This paper discusses an approach to feature logic called the structural approach. The method consists in first viewing feature structures as models (or relational structures) in the standard model theoretic sense, and then going on to consider various languages that can be interpeted on these structures and the way these languages are interrelated. It will be shown that the structural approach offers...
Bringing them all Together
, 2001
"... this paper, Jerry Seligman takes us on an interesting journey. The satisfaction denition of most modal operators is specied in terms of rstorder conditions. Hence we can always obtain a complete calculus for the basic logic characterizing any collection of such operators by appealing to a calculus ..."
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Cited by 17 (0 self)
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this paper, Jerry Seligman takes us on an interesting journey. The satisfaction denition of most modal operators is specied in terms of rstorder conditions. Hence we can always obtain a complete calculus for the basic logic characterizing any collection of such operators by appealing to a calculus which is complete for the full rstorder language. Seligman shows here that by making use of the expressiveness provided by the hybrid apparatus, we can, step by step, transform a rstorder sequent calculus into an internalized sequent calculus specically tailored for a particular hybrid fragment
Fine Grained Theories of Time
 In Working Papers of the 4 th Intl. Workshop on Semantics of Time, Space, Movement, and SpatioTemporal Reasoning
, 1992
"... this paper tries to takes it seriously. The sorted systems considered here were not developed for use in AI; they are parts of richer languages designed with the needs of natural language semantics in mind (see Blackburn [5, 8]). Only subsequently was it observed that these systems oered an interest ..."
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Cited by 9 (2 self)
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this paper tries to takes it seriously. The sorted systems considered here were not developed for use in AI; they are parts of richer languages designed with the needs of natural language semantics in mind (see Blackburn [5, 8]). Only subsequently was it observed that these systems oered an interesting perspective on temporal knowledge representation.
Path Constraints from a Modal Logic Point of View (Extended Abstract)
"... We analyze several classes of path constraints for semistructured data in a unified framework and prove some decidability and complexity results for these constraints by embedding them in Propositional Dynamic Logic. While some of our decidability results were known before, we believe that our impro ..."
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Cited by 8 (4 self)
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We analyze several classes of path constraints for semistructured data in a unified framework and prove some decidability and complexity results for these constraints by embedding them in Propositional Dynamic Logic. While some of our decidability results were known before, we believe that our improved complexity bounds are new. Our proofs, based on techniques from modal logic, shed additional light on the reasons for previously known decidability and complexity results.
On the Undecidability of Logics with . . .
, 2004
"... The evolution of Description Logics (DLs) and Propositional Dynamic Logics produced a hierarchy of decidable logics with multiple maximal elements. It would be desirable to combine different maximal logics into one superlogic, but then inference may turn out to be undecidable. Then it is importa ..."
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Cited by 1 (1 self)
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The evolution of Description Logics (DLs) and Propositional Dynamic Logics produced a hierarchy of decidable logics with multiple maximal elements. It would be desirable to combine different maximal logics into one superlogic, but then inference may turn out to be undecidable. Then it is important to characterize the decidability threshold for these logics. In this perspective, an interesting open question pointed out by Sattler and Vardi [20] is whether inference in a hybrid µcalculus with restricted forms of graded modalities is decidable, and which complexity class it belongs to. In this paper we improve a previous result [5] and prove that this calculus and the corresponding DL µALCIOfa are undecidable. We show also that nested fixpoints are not necessary for undecidability.
GEORGE GARGOV AND VALENTIN GORANKO MODAL LOGIC WITH NAMES
"... ABSTRACT. We investigate an enrichment of the propositional modal anguage with a "universal " modality n having semantics x ~ iq ~ iff Vy(y ~ ~0), and a countable set of "names " a special kind of propositional variables ranging over singleton sets of worlds. The obtained langua ..."
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ABSTRACT. We investigate an enrichment of the propositional modal anguage with a "universal " modality n having semantics x ~ iq ~ iff Vy(y ~ ~0), and a countable set of "names " a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ~cq proves to have a great expressive power. It is equivalent with respect to modal definability to another nrichment s176 of L * ~ where [] is an additional modality with the semantics x ~ [] o iff Vy(y r x ~ y ~ q~). Modeltheoretic haracterizations f modal definability in these languages are obtained. Further we consider deductive systems in ~c. Strong completeness of the normal s logics is proved with respect tomodels in which all worlds are named. Every ~~ axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly framecomplete. Problems concerning transfer of properties ([in]completeness, filtration, finite mod l property etc.) from ~ to ~ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. 1.