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10
Distributed First Order Logics
, 1998
"... ist and Wiksell, Stockholm, 1965. [ Serafini and Ghidini, 1997 ] L. Serafini and C. Ghidini. Context Based Semantics for Federated Databases. In Proceedings of the 1st International and Interdisciplinary Conference on Modeling and Using Context (CONTEXT97), pages 3345, Rio de Jeneiro, Brazil, 199 ..."
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Cited by 59 (20 self)
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ist and Wiksell, Stockholm, 1965. [ Serafini and Ghidini, 1997 ] L. Serafini and C. Ghidini. Context Based Semantics for Federated Databases. In Proceedings of the 1st International and Interdisciplinary Conference on Modeling and Using Context (CONTEXT97), pages 3345, Rio de Jeneiro, Brazil, 1997. Also IRSTTechnical Report 960902, IRST, Trento, Italy. [ Subrahmanian, 1994 ] V.S. Subrahmanian. Amalgamating Knowledge Bases. ACM Trans. Database Syst., 19(2):291331, 1994. [ Wiederhold, 1992 ] G. Wiederhold. Mediators in the architecture of future information systems. IEEE Computer, 25(3):3849, 1992. and complete calculus for DFOL based on ML systems. Finally we have compared our formalism with other formalisms for the representation and integration of distributed knowledge and reasoning systems. Acknowledgments. We thank all the people of the Mechanized Reasoning Group of IRST and DISA for useful discussions and feedb
Labelled Propositional Modal Logics: Theory and Practice
, 1996
"... We show how labelled deductive systems can be combined with a logical framework to provide a natural deduction implementation of a large and wellknown class of propositional modal logics (including K, D, T , B, S4, S4:2, KD45, S5). Our approach is modular and based on a separation between a base lo ..."
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Cited by 34 (8 self)
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We show how labelled deductive systems can be combined with a logical framework to provide a natural deduction implementation of a large and wellknown class of propositional modal logics (including K, D, T , B, S4, S4:2, KD45, S5). Our approach is modular and based on a separation between a base logic and a labelling algebra, which interact through a fixed interface. While the base logic stays fixed, different modal logics are generated by plugging in appropriate algebras. This leads to a hierarchical structuring of modal logics with inheritance of theorems. Moreover, it allows modular correctness proofs, both with respect to soundness and completeness for semantics, and faithfulness and adequacy of the implementation. We also investigate the tradeoffs in possible labelled presentations: We show that a narrow interface between the base logic and the labelling algebra supports modularity and provides an attractive prooftheory (in comparision to, e.g., semantic embedding) but limits th...
Natural deduction for firstorder hybrid logic
 Journal of Logic, Language and Information
, 2005
"... This is a companion paper to [6] where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the firstorder case. Our natural deduction system for firstorder hybrid logic can be extended with additional inference rules corresponding to ..."
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Cited by 7 (0 self)
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This is a companion paper to [6] where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the firstorder case. Our natural deduction system for firstorder hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by socalled geometric theories. We prove soundness and completeness and we prove a normalisation theorem. 1
Tacticbased theorem proving in firstorder modal and temporal logics
 University of Siena
, 2001
"... Abstract. We describe the ongoing work on a tacticbased theorem prover for FirstOrder Modal and Temporal Logics (FOTLs for the temporal ones). In formal methods, especially temporal logics play a determining role; in particular, FOTLs are natural whenever the modeled systems are infinitestate. Bu ..."
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Cited by 5 (4 self)
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Abstract. We describe the ongoing work on a tacticbased theorem prover for FirstOrder Modal and Temporal Logics (FOTLs for the temporal ones). In formal methods, especially temporal logics play a determining role; in particular, FOTLs are natural whenever the modeled systems are infinitestate. But reasoning in FOTLs is hard and few approaches have so far proved effective. Here we introduce a family of sequent calculi for firstorder modal and temporal logics which is modular in the structure of time; moreover, we present a tacticbased modal/temporal theorem prover enforcing this approach, obtained employing the higherorder logic programming language λProlog. Finally, we show some promising experimental results and raise some open issues. We believe that, together with the Proof Planning approach, our system will eventually be able to improve the state of the art of formal methods through the use of FOTLs. 1
Automated Reasoning in Quantified Modal and Temporal Logics
, 2005
"... This paper is a summary of the author’s Ph.D. thesis, concerned with automated reasoning in quantified modal and temporal logics. The relevant contributions are: (i) a sound and complete set of sequent calculi for quantified modal logics is devised; (ii) the approach is extended to the quantified te ..."
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Cited by 3 (2 self)
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This paper is a summary of the author’s Ph.D. thesis, concerned with automated reasoning in quantified modal and temporal logics. The relevant contributions are: (i) a sound and complete set of sequent calculi for quantified modal logics is devised; (ii) the approach is extended to the quantified temporal logic of linear, discrete time and a framework for doing automated reasoning via Proof Planning in it is developed; (iii) a set of promising experimental results is shown, obtained by applying the framework to the problem of Feature Interactions in telecommunication systems.
Safety and Liveness in Concurrent Pointer Programs
 in: FMCO ’06, LNCS 4111 (2006
, 2006
"... The incorrect use of pointers is one of the most common source of software errors. Concurrency has a similar characteristic. Proving the correctness of concurrent pointer manipulating programs, let alone algorithmically, is a highly nontrivial task. This paper proposes an automated verification ..."
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Cited by 3 (1 self)
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The incorrect use of pointers is one of the most common source of software errors. Concurrency has a similar characteristic. Proving the correctness of concurrent pointer manipulating programs, let alone algorithmically, is a highly nontrivial task. This paper proposes an automated verification technique for concurrent programs that manipulate linked lists. Key issues of our approach are: automata (with fairness constraints), heap abstractions that are tailored to the program and property to be checked, firstorder temporal logic, and a tableaubased modelchecking algorithm.
Labelled Modal Sequents
 In Areces and de Rijke [AdR99]. Use Your Logic 7
, 2000
"... In this paper we present a new labelled sequent calculus for modal logic. The proof method works with a more "liberal" modal language which allows inferential steps where di#erent formulas refer to different labels without moving to a particular world and there computing if the consequence holds. Wo ..."
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Cited by 2 (0 self)
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In this paper we present a new labelled sequent calculus for modal logic. The proof method works with a more "liberal" modal language which allows inferential steps where di#erent formulas refer to different labels without moving to a particular world and there computing if the consequence holds. Worldpaths can be composed, decomposed and manipulated through unification algorithms and formulas in different worlds can be compared even if they are subformulas which do not depend directly on the main connective. Accordingly, such a sequent system can provide a general definition of modal consequence relation. Finally, we briefly sketch a proof of the soundness and completeness results.
Firstorder MultiModal Deduction
"... This report aims to help provide such links by providing a set of extremely general results about firstorder multimodal deduction in terms of analytic tableaux and a prefix representation of possible worlds. We first provide sound and complete ground tableau and sequent inference systems, extendin ..."
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Cited by 1 (1 self)
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This report aims to help provide such links by providing a set of extremely general results about firstorder multimodal deduction in terms of analytic tableaux and a prefix representation of possible worlds. We first provide sound and complete ground tableau and sequent inference systems, extending and refining those presented in [Fitting and Mendelsohn, 1998] to the multimodal case. Then we show how to apply general prooftheoretic techniques to derive an equivalent calculus where Herbrand terms streamline proof search [Lincoln and Shankar, 1994]. Finally, we derive a lifted multimodal sequent inference system, which uses unification (or constraintsatisfaction) to resolve the values of variables, in the style of [Voronkov, 1996]. From one point of view, this report can be regarded as the multimodal generalization of the results presented for linear logic and firstorder modal logic in [Lincoln and Shankar, 1994, Fitting, 1996, Fitting and Mendelsohn, 1998]; alternatively, it can be seen as recasting into a modal setting the results of [Stone, 1999b], which investigates firstorder intuitionistic logic along similar lines. Formal modal logic goes back eighty years [Lewis, 1918, Lewis and Langford, 1932]. Yet according to McCarthy [McCarthy, 1997], for example, the modal logic literature still does not offer a formalism with the intensional expressive powerincluding fresh modalities defined ad hoc,and means to describe knowing what by concise and easily manipulated formulasthat is needed for knowledge representation in Artificial Intelligence. Moreover, typical results from the modal logic literature do not support the design of specialized modal inference mechanisms to solve particular knowledge representation tasks. The approach adopted here is a response t...
Labelled Quantified Modal Logics
"... . We present an approach to providing natural deduction style proof systems for a large class of quantified modal logics with varying, increasing, decreasing or constant domains of quantification. The systems we develop are modular both in the behavior of the accessibility relation and quantificatio ..."
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. We present an approach to providing natural deduction style proof systems for a large class of quantified modal logics with varying, increasing, decreasing or constant domains of quantification. The systems we develop are modular both in the behavior of the accessibility relation and quantification relative to the semantics, and in the proofs of soundness and completeness relative to that semantics. Our systems also provide the basis of simple implementations of quantified modal logics in a standard logical framework theorem prover. 1 Introduction Modal logic is an active area of research in computer science and artificial intelligence, as a language for formalizing and reasoning about, e.g., knowledge, belief, time, space, and other dynamic `state oriented' properties. The principles of propositional modal logics (PMLs) are well understood, and the relationship between semantics and proof theory captured in general metatheorems which we can exploit in developing new systems. The si...
Chapter 1 SEMANTICS FOR TEMPORAL ANNOTATED CONSTRAINT LOGIC PROGRAMMING
"... We investigate semantics of a considerable subset of Temporal Annotated Constraint Logic Programming (TACLP), a class of languages that allows us to reason about qualitative and quantitative, definite and indefinite temporal information using time points and time periods as labels for atoms. After i ..."
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We investigate semantics of a considerable subset of Temporal Annotated Constraint Logic Programming (TACLP), a class of languages that allows us to reason about qualitative and quantitative, definite and indefinite temporal information using time points and time periods as labels for atoms. After illustrating the power of TACLP with some nontrivial examples, TACLP is given two different kinds of semantics, an operational one based on metalogic (topdown semantics) and, for the first time, a fixpoint one based on an immediate consequence operator (bottomup semantics). We prove the topdown semantics to be sound and complete with respect to the bottomup semantics. Keywords: