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30
Modal Languages And Bounded Fragments Of Predicate Logic
, 1996
"... Model Theory. These are nonempty families I of partial isomorphisms between models M and N , closed under taking restrictions to smaller domains, and satisfying the usual BackandForth properties for extension with objects on either side  restricted to apply only to partial isomorphisms of size ..."
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Cited by 213 (12 self)
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Model Theory. These are nonempty families I of partial isomorphisms between models M and N , closed under taking restrictions to smaller domains, and satisfying the usual BackandForth properties for extension with objects on either side  restricted to apply only to partial isomorphisms of size at most k . 'Invariance for kpartial isomorphism' means having the same truth value at tuples of objects in any two models that are connected by a partial isomorphism in such a set. The precise sense of this is spelt out in the following proof. 21 Proof (Outline.) kvariable formulas are preserved under partial isomorphism, by a simple induction. More precisely, one proves, for any assignment A and any partial isomorphism IÎI which is defined on the Avalues for all variables x 1 , ..., x k , that M, A = f iff N , IoA = f . The crucial step in the induction is the quantifier case. Quantified variables are irrelevant to the assignment, so that the relevant partial isomorphism can be res...
Modality in Dialogue: Planning, Pragmatics and Computation
, 1998
"... Natural language generation (NLG) is first and foremost a reasoning task. In this reasoning, a system plans a communicative act that will signal key facts about the domain to the hearer. In generating action descriptions, this reasoning draws on characterizations both of the causal properties of the ..."
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Cited by 36 (9 self)
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Natural language generation (NLG) is first and foremost a reasoning task. In this reasoning, a system plans a communicative act that will signal key facts about the domain to the hearer. In generating action descriptions, this reasoning draws on characterizations both of the causal properties of the domain and the states of knowledge of the participants in the conversation. This dissertation shows how such characterizations can be specified declaratively and accessed efficiently in NLG. The heart of this dissertation is a study of logical statements about knowledge and action in modal logic. By investigating the prooftheory of modal logic from a logic programming point of view, I show how many kinds of modal statements can be seen as straightforward instructions for computationally manageable search, just as Prolog clauses can. These modal statements provide sufficient expressive resources for an NLG system to represent the effects of actions in the world or to model an addressee whose knowledge in some respects exceeds and in other respects falls short of its own. To illustrate the use of such statements, I describe how the SPUD sentence planner exploits a modal knowledge base to
A Tableau Calculus for Multimodal Logics and Some (Un)Decidability Results
 IN PROC. OF TABLEAUX98
, 1998
"... In this paper we present a prefixed analytic tableau calculus for a class of normal multimodal logics and we present some results about decidability and undecidability of this class. The class is characterized by axioms of the form [t 1 ] : : : [t n ]' oe [s1 ] : : : [sm ]', called inclusion axio ..."
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Cited by 24 (8 self)
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In this paper we present a prefixed analytic tableau calculus for a class of normal multimodal logics and we present some results about decidability and undecidability of this class. The class is characterized by axioms of the form [t 1 ] : : : [t n ]' oe [s1 ] : : : [sm ]', called inclusion axioms, where the t i 's and s j 's are constants. This class of logics, called grammar logics, was introduced for the first time by Farinas del Cerro and Penttonen to simulate the behaviour of grammars in modal logics, and includes some wellknown modal systems. The prefixed tableau method is used to prove the undecidability of modal systems based on unrestricted, context sensitive, and context free grammars. Moreover, we show that the class of modal logics, based on rightregular grammars, are decidable by means of the filtration methods, by defining an extension of the FischerLadner closure.
Planning from Second Principles
 Artificial Intelligence
, 1996
"... Planning from second principles by reusing and modifying plans is one way of improving the efficiency of planning systems. In this paper, we study it in the general framework of deductive planning and develop a logical formalization of planning from second principles, which relies on a systematic ..."
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Cited by 22 (1 self)
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Planning from second principles by reusing and modifying plans is one way of improving the efficiency of planning systems. In this paper, we study it in the general framework of deductive planning and develop a logical formalization of planning from second principles, which relies on a systematic decomposition of the planning process. Deductive inference processes with clearly defined semantics formalize each of the subtasks a second principles planner has to address. Plan modification, which comprises matching and adaptation tasks, is based on a deductive approach yielding provably correct modified plans. Description logics are introduced as query languages to plan libraries, which leads to a novel and efficient solution to the indexing problem in casebased reasoning. Apart from sequential plans, this approach enables a planner to reuse and modify complex plans containing control structures like conditionals and loops. 1 Introduction Planning from first principles generat...
A SetTheoretic Translation Method for Polymodal Logics
, 1995
"... The paper presents a settheoretic translation method for polymodal logics that reduces the derivability problem of a large class of propositional polymodal logics to the derivability problem of a very weak firstorder set theory\Omega\Gamma Unlike most existing translation methods, the one we propos ..."
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Cited by 19 (12 self)
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The paper presents a settheoretic translation method for polymodal logics that reduces the derivability problem of a large class of propositional polymodal logics to the derivability problem of a very weak firstorder set theory\Omega\Gamma Unlike most existing translation methods, the one we proposed applies to any normal complete finitelyaxiomatizable polymodal logic, regardless if it is firstorder complete or if an explicit semantics is available for it. Moreover, the finite axiomatizability of\Omega makes it possible to implement mechanical proof search procedures via the deduction theorem or more specialized and efficient techniques. In the last part of the paper, we briefly discuss the application of set T resolution to support automated derivability in (a suitable extension of) \Omega\Gamma This work has been supported by funds MURST 40% and 60%. The second author was supported by a grant from the Italian Consiglio Nazionale delle Ricerche (CNR). 1 Introduction The paper...
A Framework for Modal Logic Programming
 In Joint International Conference and Symposium on Logic Programming
, 1996
"... In this paper we present a framework for developing modal extensions of logic programming, which are parametric with respect to the properties chosen for the modalities and which allow sequences of modalities of the form [t], where t is a term of the language, to occur in front of clauses, goals and ..."
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Cited by 18 (3 self)
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In this paper we present a framework for developing modal extensions of logic programming, which are parametric with respect to the properties chosen for the modalities and which allow sequences of modalities of the form [t], where t is a term of the language, to occur in front of clauses, goals and clause heads. The properties of modalities are specified by a set A of inclusion axioms of the form [t 1 ] : : : [t n ]ff oe [s 1 ] : : : [s m ]ff. The language can deal with many of the wellknown modal systems and several examples are provided. Due to its features, it is particularly suitable for performing epistemic reasoning, defining parametric and nested modules, describing inheritance in a hierarchy of classes and reasoning about actions. A goal directed proof procedure of the language is presented, which is modular with respect to the properties of modalities. Moreover, we define a fixpoint semantics, by generalizing the standard construction for Horn clauses, which is used to prov...
Labelled Tableaux for MultiModal Logics
 Theorem Proving with Analytic
, 1995
"... this paper we present a tableaulike proof system for multimodal logics based on D'Agostino and Mondadori's classical refutation system KE [DM94]. The proposed system, that we call KEM , works for the logics S5A and S5P(n) which have been devised by Mayer and van der Hoek [MvH92] for formalizing th ..."
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Cited by 17 (9 self)
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this paper we present a tableaulike proof system for multimodal logics based on D'Agostino and Mondadori's classical refutation system KE [DM94]. The proposed system, that we call KEM , works for the logics S5A and S5P(n) which have been devised by Mayer and van der Hoek [MvH92] for formalizing the notions of actuality and preference. We shall also show how KEM works with the normal modal logics K45, D45, and S5 which are frequently used as bases for epistemic operators  knowledge, belief (see, for example [Hoe93, Wan90]), and we shall briefly sketch how to combine knowledge and belief in a multiagent setting through KEM modularity
A MultiLevel Approach to program Synthesis
, 1998
"... We present an approach to a coherent program synthesis system which integrates a variety of interactively controlled and automated techniques from theorem proving and algorithm design at different levels of abstraction. Besides providing an overall view we summarize the individual research results ..."
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Cited by 13 (9 self)
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We present an approach to a coherent program synthesis system which integrates a variety of interactively controlled and automated techniques from theorem proving and algorithm design at different levels of abstraction. Besides providing an overall view we summarize the individual research results achieved in the course of this development.
Modal Deduction in SecondOrder Logic and Set Theory
 Journal of Logic and Computation
, 1997
"... We investigate modal deduction through translation into standard logic and set theory. Derivability in the minimal modal logic is captured precisely by translation into a weak, computationally attractive set theory \Omega\Gamma This approach is shown equivalent to working with standard firstorder t ..."
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Cited by 11 (7 self)
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We investigate modal deduction through translation into standard logic and set theory. Derivability in the minimal modal logic is captured precisely by translation into a weak, computationally attractive set theory \Omega\Gamma This approach is shown equivalent to working with standard firstorder translations of modal formulas in a theory of general frames. Next, deduction in a more powerful secondorder logic of general frames is shown equivalent with settheoretic derivability in an `admissible variant' of \Omega\Gamma Our methods are mainly modeltheoretic and settheoretic, and they admit extension to richer languages than that of basic modal logic. 1 Introduction We are interested in analyzing general deduction for modal formulae [4]. The standard systems used for this purpose are the socalled "minimal modal logic" K or, if one wants to work over general frames (as we do), the system K s obtained from K adding a substitution rule. We do not consider special purpose calculi for ...
A Modal Extension of Logic Programming: Modularity, Beliefs and Hypothetical Reasoning
, 1995
"... In this paper we present a modal extension of logic programming, which allows both multiple modalities and embedded implications. We show that this extension is well suited for structuring knowledge and, specifically, for defining module constructs within programs, for representing agents beliefs, a ..."
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Cited by 10 (2 self)
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In this paper we present a modal extension of logic programming, which allows both multiple modalities and embedded implications. We show that this extension is well suited for structuring knowledge and, specifically, for defining module constructs within programs, for representing agents beliefs, and also for hypothetical reasoning. The language contains modalities [a i ] to represent agent beliefs, and a modality 2 which is a kind of common knowledge operator. It allows sequences of modalities to occur in front of clauses, goals and clause heads, and hypothetical implications to occur in goals and in clause bodies. A goal directed proof procedure of the language is presented, and several examples of its use for defining modules are given. In particular, the language is shown to capture different proposal for module definition and composition presented in the literature. The modal logic, of which our programming language is a clausal fragment, is introduced through its Kripke semantic...