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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 37 (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
Deciding Provability of Linear Logic Formulas
 Advances in Linear Logic
, 1994
"... Introduction There are many interesting fragments of linear logic worthy of study in their own right, most described by the connectives which they employ. Full linear logic includes all the logical connectives, which come in three dual pairs: the exponentials ! and ?, the additives & and \Phi, ..."
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Introduction There are many interesting fragments of linear logic worthy of study in their own right, most described by the connectives which they employ. Full linear logic includes all the logical connectives, which come in three dual pairs: the exponentials ! and ?, the additives & and \Phi, and the multiplicatives\Omega and . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ . SRI International Computer Science Laboratory, Menlo Park CA 94025 USA. Work supported under NSF Grant CCR9224858. lincoln@csl.sri.com http://www.csl.sri.com/lincoln/lincoln.html Patrick Lincoln For the most part we will consider fragments of linear logic built up using these connectives in any combination. For example, full linear logic formulas may employ any connective, while multiplic
Interpreting Strands in Linear Logic
, 2000
"... The adoption of the DolevYao model, an abstraction of security protocols that supports symbolic reasoning, is responsible for many successes in protocol analysis. In particular, it has enabled using logic effectively to reason about protocols. One recent framework for expressing the basic assumptio ..."
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Cited by 24 (14 self)
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The adoption of the DolevYao model, an abstraction of security protocols that supports symbolic reasoning, is responsible for many successes in protocol analysis. In particular, it has enabled using logic effectively to reason about protocols. One recent framework for expressing the basic assumptions of the DolevYao model is given by strand spaces, certain directed graphs whose structure reflects causal interactions among protocol participants. We represent strand constructions as relatively simple formulas in firstorder linear logic, a refinement of traditional logic known for an intrinsic and natural accounting of process states, events, and resources. The proposed encoding is shown to be sound and complete. Interestingly, this encoding differs from the multiset rewriting definition of the DolevYao model, which is also based on linear logic. This raises the possibility that the multiset rewriting framework may differ from strand spaces in some subtle way, although the two settings are known to agree on the basic secrecy property. 1 Introduction In recent years, a variety of methods have been developed for analyzing and reasoning about protocols based on cryptographic primitives. Although there are many differences among these proposals, most current formal approaches use the socalled "DolevYao" model of adversary capabilities, which appears to be drawn from positions taken in [34] and from a simplified model presented in [11]. In this idealized setting, a protocol adversary is allowed to nondeterministically choose among possible actions. Messages are composed of indivisible abstract values, not sequences of bits, and encryption is modeled in an idealized way. The adversary may only send messages comprised of data it "knows" as the result of overhearing past transmissions.
On ProofSearch in Intuitionistic Logic with Equality, or Back to Simultaneous Rigid EUnification
 Automated Deduction  CADE13
, 1996
"... We characterize provability in intuitionistic logic with equality in terms of a constraint calculus. This characterization uncovers close connections between provability in intuitionistic logic with equality and solutions to simultaneous rigid Eunification. We show that the problem of existence of ..."
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Cited by 19 (9 self)
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We characterize provability in intuitionistic logic with equality in terms of a constraint calculus. This characterization uncovers close connections between provability in intuitionistic logic with equality and solutions to simultaneous rigid Eunification. We show that the problem of existence of a sequent proof with a given skeleton is polynomialtime equivalent to simultaneous rigid Eunifiability. This gives us a proof procedure for intuitionistic logic with equality modulo simultaneous rigid Eunification. We also show that simultaneous rigid Eunifiability is polynomialtime reducible to intuitionistic logic with equality. Thus, any proof procedure for intuitionistic logic with equality can be considered as a procedure for simultaneous rigid Eunifiability. In turn, any procedure for simultaneous rigid Eunifiability gives a procedure for establishing provability in intuitionistic logic with equality. 2 2 Copyright c fl 1995, 1996 Andrei Voronkov. This technical report and ot...
The Undecidability of Second Order Multiplicative Linear Logic
, 1996
"... The multiplicative fragment of second order propositional linear logic is shown to be undecidable. Introduction Decision problems for propositional (quantifierfree) linear logic were first studied by Lincoln et al. [LMSS]. In referring to linear logic fragments, let M stand for multiplicatives, A ..."
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Cited by 14 (3 self)
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The multiplicative fragment of second order propositional linear logic is shown to be undecidable. Introduction Decision problems for propositional (quantifierfree) linear logic were first studied by Lincoln et al. [LMSS]. In referring to linear logic fragments, let M stand for multiplicatives, A for additives, E for exponentials (or modalities), 1 for first order quantifiers, 2 for second order propositional quantifiers, and I for "intuitionistic" version. In [LMSS] it was shown that full propositional linear logic is undecidable and that MALL is PSPACEcomplete. The main problems left open in [LMSS] were the NPcompleteness of MLL, the decidability of MELL, and the decidability of various fragments of propositional linear logic without exponentials but extended with second order propositional quantifiers. The decision problem for MELL is still open, but almost all the other problems have been solved: ffl The NPcompleteness of MLL has been obtained by Kanovich [K1]. Moreover, Linco...
Deterministic Resource Management for the Linear Logic Programming Language Lygon
, 1994
"... Recently there has been significant interest in the logic programming community in linear logic, a logic designed with bounded resources in mind. As linear logic is a generalisation of classical logic, a logic programming language based on linear logic subsumes and extends (pure) Prolog. One such la ..."
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Cited by 14 (5 self)
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Recently there has been significant interest in the logic programming community in linear logic, a logic designed with bounded resources in mind. As linear logic is a generalisation of classical logic, a logic programming language based on linear logic subsumes and extends (pure) Prolog. One such language is Lygon, a language based on a certain kind of proof in the linear sequent calculus. However these proofs, whilst providing a logical characterization of the language, still retain some of the nondeterminism of the sequent calculus, and hence require further analysis before an implementation can be attempted. In this report we define and discuss a more detailed proof system, which is more deterministic than the original. In particular, this system handles the allocation of resources to different branches of the proof in a lazy manner. The resulting system differs significantly from the original sequent calculus, and so we discuss its properties in some detail. We prove the soundness...
On GoalDirected Provability in Classical Logic
, 1994
"... this paper we explore the possibilities for a notion of goaldirected proof in classical logic. The technical point to consider is how to deal with the multipleconclusioned nature of classical sequents, i.e. that classical succedents may contain more than one formula. This means that there may be mo ..."
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Cited by 5 (1 self)
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this paper we explore the possibilities for a notion of goaldirected proof in classical logic. The technical point to consider is how to deal with the multipleconclusioned nature of classical sequents, i.e. that classical succedents may contain more than one formula. This means that there may be more than one "candidate" right rule, as there may be several nonatomic formulae in the succedent, and so a choice has to be made as to which formula is to be reduced in the next step. The question of whether this choice may be free or restricted is one of the key decisions to be made. The free choice, i.e. that the order in which the formulae are reduced does not matter, will clearly constrain the logic programming language more than the restricted, one, and is arguably more declarative; on the other hand, the weaker notion is arguably more goaldirected, and there is no obvious reason to insist on the stronger version. We will refer to the free choice as rightreductive proofs, and to the restricted one as rightdirected proofs. Thus there seems to be more than one notion of goaldirected proof in classical logic, and clearly the corresponding logic programming languages may differ according to which class of proofs is used. However, as we shall see, there are do not seem to be any "interesting" languages for which the weaker notion is complete but the stronger one is not, and so it appears the stronger version (which requires that all right rules permute over each other) is the more useful notion.
Efficient constraints on possible worlds for reasoning about necessity
 University of Pennsylvania. Submitted
, 1997
"... Modal logics offer natural, declarative representations for describing both the modular structure of logical specifications and the attitudes and behaviors of agents. The results of this paper further the goal of building practical, efficient reasoning systems using modal logics. The key problem in ..."
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Modal logics offer natural, declarative representations for describing both the modular structure of logical specifications and the attitudes and behaviors of agents. The results of this paper further the goal of building practical, efficient reasoning systems using modal logics. The key problem in modal deduction is reasoning about the world in a model (or scope in a proof) at which an inference rule is applied—a potentially hard problem. This paper investigates the use of partialorder mechanisms to maintain constraints on the application of modal rules in proof search in restricted languages. The main result is a simple, incremental polynomialtime algorithm to correctly order rules in proof trees for combinations of K, K4, T and S4 necessity operators governed by a variety of interactions, assuming an encoding of negation using a scoped constant?. This contrasts with previous equational unification methods, which have exponential performance in general because they simply guess among possible intercalations of modal operators. The new, fast algorithm is appropriate for use in a wide variety of applications of modal logic, from planning to logic programming. Content area: Reasoning Techniques—deduction, efficiency and complexity. 1
Representing Scope in Intuitionistic Deductions
 THEORETICAL COMPUTER SCIENCE
, 1997
"... Intuitionistic proofs can be segmented into scopes which describe when assumptions can be used. In standard descriptions of intuitionistic logic, these scopes occupy contiguous regions of proofs. This leads to an explosion in the search space for automated deduction, because of the difficulty of pla ..."
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Intuitionistic proofs can be segmented into scopes which describe when assumptions can be used. In standard descriptions of intuitionistic logic, these scopes occupy contiguous regions of proofs. This leads to an explosion in the search space for automated deduction, because of the difficulty of planning to apply a rule inside a particular scoped region of the proof. This paper investigates an alternative representation which assigns scope explicitly to formulas, and which is inspired in part by semanticsbased translation methods for modal deduction. This calculus is simple and is justified by direct prooftheoretic arguments that transform proofs in the calculus so that scopes match standard descriptions. A Herbrand theorem, established straightforwardly, lifts this calculus to incorporate unification. The resulting system has no impermutabilities whatsoeverrules of inference may be used equivalently anywhere in the proof. Nevertheless, a natural specification describes how terms...