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16
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.
An Abductive Proof Procedure for Reasoning about Actions in Modal Logic P r o g r a m m i n g
, 1997
"... . In this paper we propose a modal approach for reasoning about actions in a logic programming framework. We introduce a modal language which makes use of abductive assumptions to deal with persistency, and provides a solution to the ramification problem, by allowing oneway "causal rules" to be ..."
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Cited by 16 (10 self)
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. In this paper we propose a modal approach for reasoning about actions in a logic programming framework. We introduce a modal language which makes use of abductive assumptions to deal with persistency, and provides a solution to the ramification problem, by allowing oneway "causal rules" to be defined among fluents. We define the abductive semantics of the language and a goal directed abductive proof procedure to compute abductive solutions for a goal from a given domain description. Both the semantics and the procedure are defined within the argumentation framework. In particular, we focus on a specific semantics, which is essentially an extension of Dung's admissibility semantics to a modal setting. The proof procedure is proved to be sound with respect to this semantics. 1 Introduction Reasoning about a world dynamically changing under effects of actions is one of the central problems of knowledge representation. In this context, starting from Gelfond and Lifschitz' w...
Multimodal logic programming
 Theoretical Computer Science
, 2006
"... We give a framework for developing the least model semantics, fixpoint semantics, and SLDresolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. ∀x ∃y Ri(x, y)) and some classical firstorder Horn formulas. Our approach is dir ..."
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Cited by 12 (7 self)
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We give a framework for developing the least model semantics, fixpoint semantics, and SLDresolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. ∀x ∃y Ri(x, y)) and some classical firstorder Horn formulas. Our approach is direct and no special restriction on occurrences of ✷i and ✸i is required. We apply our framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T, B, 4, 5 (in the form, e.g., 4: ✷iϕ → ✷j✷kϕ) and I: ✷iϕ → ✷jϕ. Another part of the work is devoted to programming in multimodal logics intended for reasoning about multidegree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multiagent systems. For that we also use the framework, and although these latter logics belong to the mentioned class of basic serial multimodal logics, the special SLDresolution calculi proposed for them are more efficient.
A Modal Programming Language for Representing Complex Actions
 In Proc. DYNAMICS'98: Transactions and Change in Logic Databases
, 1998
"... In this paper we propose a modal approach for reasoning about dynamic domains in a logic programming setting. In particular we define a language, called DyLOG, in which actions are naturally represented by modal operators. DyLOG is a language for reasoning about actions which allows to deal with ..."
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Cited by 11 (6 self)
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In this paper we propose a modal approach for reasoning about dynamic domains in a logic programming setting. In particular we define a language, called DyLOG, in which actions are naturally represented by modal operators. DyLOG is a language for reasoning about actions which allows to deal with ramifications and to define procedures to build complex actions from elementary ones. Procedure definitions can be easily specified in the modal language by introducing suitable axioms. In the language the frame problem is given a nonmonotonic solution by making use of persistency assumptions in the context of an abductive characterization. Moreover, a goal directed proof procedure is defined, which allows to compute a query from a given dynamic domain description. 1 Introduction Reasoning about the effects of actions in a dynamically changing world is one of the main problems which must be faced by intelligent agents. Most of the approaches which have been developed to model action...
Computational modal logic
 Handbook of Modal Logic
, 2006
"... 2 Syntax, semantics, and reasoning problems of modal logics........................... 3 3 Translationbased methods........................................... 6 3.1 Local satisfiability in multi modal Kn................................... 6 3.2 Global satisfiability, nonlogical axioms, transitive ..."
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Cited by 10 (3 self)
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2 Syntax, semantics, and reasoning problems of modal logics........................... 3 3 Translationbased methods........................................... 6 3.1 Local satisfiability in multi modal Kn................................... 6 3.2 Global satisfiability, nonlogical axioms, transitive modalities, and K4n................. 20
Multimodal and Intuitionistic Logics in Simple Type Theory
"... We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational inve ..."
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Cited by 9 (9 self)
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We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various nonclassical logics. We report some experiments using the higherorder automated theorem prover LEOII.
Temporal and Modal Logic Programming Languages
 In A. Kent and J.G. Williams (Eds.), Encyclopedia of Microcomputers
, 2001
"... Temporal and modal logics have been used in many applications in Arti cial Intelligence and Computer Science for the manipulation of information with timedependent or, in general, contextdependent properties. Knowledge representation and reasoning, temporal planning, simulation, temporal veri catio ..."
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Cited by 6 (2 self)
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Temporal and modal logics have been used in many applications in Arti cial Intelligence and Computer Science for the manipulation of information with timedependent or, in general, contextdependent properties. Knowledge representation and reasoning, temporal planning, simulation, temporal veri cation, and description of agent systems, are among the applications for which temporal and modal logics have been proven useful. Programming languages based on Temporal or Modal Logics, provide powerful executable formalisms for implementing such applications. In this article we introduce the basic notions behind temporal and modal logic programming languages. We brie y present representative temporal and modal logic programming languages and give examples of their use.
Reasoning about epistemic states of agents by modal logic programming
 Proceedings of CLIMA VI, LNAI 3900
, 2006
"... Abstract. Modal logic programming is one of appropriate approaches to deal with reasoning about epistemic states of agents. We specify here the least model semantics, the fixpoint semantics, and an SLDresolution calculus for modal logic programs in the multimodal logic KD4Ig5a, which is intended fo ..."
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Cited by 6 (6 self)
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Abstract. Modal logic programming is one of appropriate approaches to deal with reasoning about epistemic states of agents. We specify here the least model semantics, the fixpoint semantics, and an SLDresolution calculus for modal logic programs in the multimodal logic KD4Ig5a, which is intended for reasoning about belief and common belief of agents. We prove that the presented SLDresolution calculus is sound and complete. We also present a formalization of the wise men puzzle using a modal logic program in KD4Ig5a. This shows that it is worth to study modal logic programming for multiagent systems. 1
Constructing finite least Kripke models for positive logic programs in serial regular grammar logics
 Logic Journal of the IGPL
"... A serial contextfree grammar logic is a normal multimodal logic L characterized by the seriality axioms and a set of inclusion axioms of the form ✷tϕ → ✷s1... ✷skϕ. Such an inclusion axiom corresponds to the grammar rule t → s1... sk. Thus the inclusion axioms of L capture a contextfree grammar G( ..."
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Cited by 6 (4 self)
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A serial contextfree grammar logic is a normal multimodal logic L characterized by the seriality axioms and a set of inclusion axioms of the form ✷tϕ → ✷s1... ✷skϕ. Such an inclusion axiom corresponds to the grammar rule t → s1... sk. Thus the inclusion axioms of L capture a contextfree grammar G(L). If for every modal index t, the set of words derivable from t using G(L) is a regular language, then L is a serial regular grammar logic. In this paper, we present an algorithm that, given a positive multimodal logic program P and a set of finite automata specifying a serial regular grammar logic L, constructs a finite least Lmodel of P. (A model M is less than or equal to model M ′ if for every positive formula ϕ, if M  = ϕ then M ′  = ϕ.) A least Lmodel M of P has the property that for every positive formula ϕ, P  = ϕ iff M  = ϕ. The algorithm runs in exponential time and returns a model with size 2 O(n3). We give examples of P and L, for both of the case when L is fixed or P is fixed, such that every finite least Lmodel of P must have size 2 Ω(n). We also prove that if G is a contextfree grammar and L is the serial grammar logic corresponding to G then there exists a finite least Lmodel of ✷sp iff the set of words derivable from s using G is a regular language. 1