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Complexity and Expressive Power of Logic Programming
, 1997
"... This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results ..."
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Cited by 281 (57 self)
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This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.
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
Towards a formal foundation for domain specific modeling languages
 Proceedings of the Sixth ACM International Conference on Embedded Software (EMSOFT’06
, 2006
"... Embedded system design is inherently domain specific and typically model driven. As a result, design methodologies like OMG’s model driven architecture (MDA) and model integrated computing (MIC) evolved to support domain specific modeling languages (DSMLs). The success of the DSML approach has encou ..."
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Cited by 14 (10 self)
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Embedded system design is inherently domain specific and typically model driven. As a result, design methodologies like OMG’s model driven architecture (MDA) and model integrated computing (MIC) evolved to support domain specific modeling languages (DSMLs). The success of the DSML approach has encouraged work on the heterogeneous composition of DSMLs, model transformations between DSMLs, approximations of formal properties within DSMLs, and reuse of DSML semantics. However, in the effort to produce a mature design approach that can handle both the structural and behavioral semantics of embedded system design, many foundational issues concerning DSMLs have been overlooked. In this paper we present a formal foundation for DSMLs and for their construction within metamodeling frameworks. This foundation allows us to algorithmically decide if two DSMLs or metamodels are equivalent, if model transformations preserve properties, and if metamodeling frameworks have metametamodels. These results are key to building correct embedded systems with DSMLs.
A Modal Herbrand Theorem
, 1996
"... We state and prove a modal Herbrand theorem that is, we believe, a more natural analog of the classical version than has appeared before. The statement itself requires the enlargement of the usual machinery of firstorder modal logic  we use the device of predicate abstraction, something that has ..."
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Cited by 7 (3 self)
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We state and prove a modal Herbrand theorem that is, we believe, a more natural analog of the classical version than has appeared before. The statement itself requires the enlargement of the usual machinery of firstorder modal logic  we use the device of predicate abstraction, something that has been considered elsewhere as well. This expands the expressive power of modal logic in a natural way. Our proof of the modal version of Herbrand's theorem uses a tableau system that takes predicate abstraction into account. It is somewhat simpler than other systems for the same purpose that have previously appeared. 1 Introduction In classical logic, Herbrand's famous theorem of 1930 plays many roles. Herbrand seems to have thought of it as something like a constructive completeness theorem [12, 13]. Robinson cited it as the foundation of automated theorem proving [15]. It has been applied to derive results on decidability [3]. But despite its fundamental nature, it has remained remarkably...
Nonmonotonic Reasoning
 In Proc
, 1993
"... Classical logic is the study of ”safe ” formal reasoning. Western Philosophers developed classical logic over a period of thirtythree centuries after its introduction in the form of syllogistic by Aristotle [1] in the third century B. C. Beginning in the nineteenth century with De Morgan [2] and B ..."
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Cited by 5 (0 self)
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Classical logic is the study of ”safe ” formal reasoning. Western Philosophers developed classical logic over a period of thirtythree centuries after its introduction in the form of syllogistic by Aristotle [1] in the third century B. C. Beginning in the nineteenth century with De Morgan [2] and Boole [3], responsibility for the development of classical logic moved from the philosophical to the mathematical community.
Hilbert’s Program Then and Now
, 2005
"... Hilbert’s program is, in the first instance, a proposal and a research program in the philosophy and foundations of mathematics. It was formulated in the early 1920s by German mathematician David Hilbert (1862–1943), and was pursued by him and his collaborators at the University of Göttingen and els ..."
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Cited by 4 (0 self)
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Hilbert’s program is, in the first instance, a proposal and a research program in the philosophy and foundations of mathematics. It was formulated in the early 1920s by German mathematician David Hilbert (1862–1943), and was pursued by him and his collaborators at the University of Göttingen and elsewhere in the 1920s
Hilbert’s “Verunglückter Beweis,” the first epsilon theorem and consistency proofs. History and Philosophy of Logic
"... Abstract. On the face of it, Hilbert’s Program was concerned with proving consistency of mathematical systems in a finitary way. This was to be accomplished by showing that that these systems are conservative over finitistically interpretable and obviously sound quantifierfree subsystems. One propo ..."
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Cited by 3 (2 self)
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Abstract. On the face of it, Hilbert’s Program was concerned with proving consistency of mathematical systems in a finitary way. This was to be accomplished by showing that that these systems are conservative over finitistically interpretable and obviously sound quantifierfree subsystems. One proposed method of giving such proofs is Hilbert’s epsilonsubstitution method. There was, however, a second approach which was not refelected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert’s first epsilon theorem and a certain “general consistency result. ” An analysis of this socalled “failed proof ” lends further support to an interpretation of Hilbert according to which he was expressly concerned with conservatitvity proofs, even though his publications only mention consistency as the main question. §1. Introduction. The aim of Hilbert’s program for consistency proofs in the 1920s is well known: to formalize mathematics, and to give finitistic consistency proofs of these systems and thus to put mathematics on a “secure foundation.” What is perhaps less well known is exactly how Hilbert thought this should be carried out. Over ten years before Gentzen developed sequent calculus formalizations