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32
Parametric Shape Analysis via 3Valued Logic
, 1999
"... Shape Analysis concerns the problem of determining "shape invariants"... ..."
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Cited by 539 (71 self)
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Shape Analysis concerns the problem of determining "shape invariants"...
The Complexity of Concept Languages
, 1995
"... The basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies, and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called concept ..."
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Cited by 231 (33 self)
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The basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies, and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called concept language (or description logic), which is given welldefined settheoretic semantics. The efficiency of reasoning has often been advocated as a primary motivation for the use of such systems. Deduction methods and computational properties of reasoning problems in concept languages are the subject of this paper. The main contributions of the paper are: (1) a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages; (2) the algorithms for these inferences that comply with the worstcase complexity of the reasoning task they perform.
Fibring of logics as a categorial construction
 Journal of Logic and Computation
, 1999
"... Much attention has been given recently to the mechanism of fibring of logics, allowing free mixing of the connectives and using proof rules from both logics. Fibring seems to be a rather useful and general form of combination of logics that deserves detailed study. It is now well understood at the p ..."
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Cited by 51 (31 self)
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Much attention has been given recently to the mechanism of fibring of logics, allowing free mixing of the connectives and using proof rules from both logics. Fibring seems to be a rather useful and general form of combination of logics that deserves detailed study. It is now well understood at the prooftheoretic level. However, the semantics of fibring is still insufficiently understood. Herein we provide a categorial definition of both prooftheoretic and modeltheoretic fibring for logics without terms. To this end, we introduce the categories of Hilbert calculi, interpretation systems and logic system presentations. By choosing appropriate notions of morphism it is possible to obtain pure fibring as a coproduct. Fibring with shared symbols is then easily obtained by cocartesian lifting from the category of signatures. Soundness is shown to be preserved by these constructions. We illustrate the constructions within propositional modal logic.
Predicative Recursion and Computational Complexity
, 1992
"... The purpose of this thesis is to give a "foundational" characterization of some common complexity classes. Such a characterization is distinguished by the fact that no explicit resource bounds are used. For example, we characterize the polynomial time computable functions without making any direct r ..."
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Cited by 45 (3 self)
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The purpose of this thesis is to give a "foundational" characterization of some common complexity classes. Such a characterization is distinguished by the fact that no explicit resource bounds are used. For example, we characterize the polynomial time computable functions without making any direct reference to polynomials, time, or even computation. Complexity classes characterized in this way include polynomial time, the functional polytime hierarchy, the logspace decidable problems, and NC. After developing these "resource free" definitions, we apply them to redeveloping the feasible logical system of Cook and Urquhart, and show how this firstorder system relates to the secondorder system of Leivant. The connection is an interesting one since the systems were defined independently and have what appear to be very different rules for the principle of induction. Furthermore it is interesting to see, albeit in a very specific context, how to retract a second order statement, ("inducti...
GentzenType Systems, Resolution And Tableaux
 Journal of Automated Reasoning
, 1993
"... Introduction In advanced books and courses on logic (e.g. [Sm], [BM]) Gentzentype systems or their dual, tableaux, are described as techniques for showing validity of formulae which are more practical than the usual Hilberttype formalisms. People who have learnt these methods often wonder why the ..."
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Cited by 33 (12 self)
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Introduction In advanced books and courses on logic (e.g. [Sm], [BM]) Gentzentype systems or their dual, tableaux, are described as techniques for showing validity of formulae which are more practical than the usual Hilberttype formalisms. People who have learnt these methods often wonder why the Automated Reasoning community seems to ignore them and prefers instead the resolution method. Some of the classical books on AD (such as [CL], [Lo]) do not mention these methods at all. Others (such as [Ro]) do, but the connections and reasons for preference remain unclear after reading them (at least to the present author, and obviously also the authors of [OS], in which a theoremprover, based exclusively on tableaux, is described). The confusion becomes greater when the reader is introduced to Kowalski's form of a clause ([Ko], [Bu]), which is nothing but a Gentzen's sequent of atomic formulae, and when he realizes that resolution is just a form of a Cut, and so that while the<F1
A Logical View Of Concurrent Constraint Programming
, 1995
"... . Concurrent Constraint Programming (CCP) has been the subject of growing interest as the focus of a new paradigm for concurrent computation. Like logic programming it claims close relations to logic. In fact CCP languages are logics in a certain sense that we make precise in this paper. In recent ..."
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Cited by 23 (4 self)
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. Concurrent Constraint Programming (CCP) has been the subject of growing interest as the focus of a new paradigm for concurrent computation. Like logic programming it claims close relations to logic. In fact CCP languages are logics in a certain sense that we make precise in this paper. In recent work it was shown that the denotational semantics of determinate concurrent constraint programming languages forms a fibred categorical structure called a hyperdoctrine, which is used as the basis of the categorical formulation of firstorder logic. What this shows is that the combinators of determinate CCP can be viewed as logical connectives. In this paper we extend these ideas to the operational semantics of such languages and thus make available similar analogies for a much broader variety of languages including indeterminate CCP languages and concurrent blockstructured imperative languages. CR Classification: F3.1, F3.2, D1.3, D3.3 Key words: Concurrent constraint programming, simula...
COCOLOG: A Conditional Observer and Controller Logic for Finite Machines
, 1994
"... The problem of observation and control for partially observed inputstateoutput machines is formulated in terms of a tree of first order logical theories. A set of first order languages for the description of the controlled evolution and state estimation of any given machine M is specified; furthe ..."
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Cited by 17 (4 self)
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The problem of observation and control for partially observed inputstateoutput machines is formulated in terms of a tree of first order logical theories. A set of first order languages for the description of the controlled evolution and state estimation of any given machine M is specified; further, extralogical conditional control rules are formulated so that closed loop control actions occur when extralogically specified past observation dependent conditions are fulfilled. In particular, conditional control rules may include commands that steer the system state from a current partially observed state (estimate) to a target state, if such a sequence of controls can be proven to exist. Starting from a general theory of M at the initial instant, observations on the inputoutput behaviour of the system at any later instant are accepted by the system as new axioms; these are then used together with the previously generated theory to generate the current theory. The acronym COCOLOG is ...
Inductive Definability and the Situation Calculus
 In Transaction and Change in Logic Databases
, 1998
"... . We explore the situation calculus within the framework of inductive definability. A consequence of this view of the situation calculus is to establish direct connections with different variants of the  calculus [Park, 1970; Hitchcock and Park, 1973; Pratt, 1981; Kozen, 1983; Emerson and Clark ..."
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Cited by 12 (1 self)
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. We explore the situation calculus within the framework of inductive definability. A consequence of this view of the situation calculus is to establish direct connections with different variants of the  calculus [Park, 1970; Hitchcock and Park, 1973; Pratt, 1981; Kozen, 1983; Emerson and Clarke, 1980], structural operational semantics of concurrent processes [Plotkin, 1981], and logic programming [Apt, 1990]. First we show that the induction principle on situations [Reiter, 1993] is implied by an inductive definition of the set of situations. Then we consider the frame problem from the point of view of inductive definability and by defining fluents inductively we obtain essentially the same form of successor state axioms as [Reiter, 1991]. Our approach allows extending this result to the case where ramification constraints are present. Finally we demonstrate a method of applying inductive definitions for computing fixed point properties of GOLOG programs. 1 Introduction...
Lp, A Logic for Representing and Reasoning with Statistical Knowledge
, 1990
"... This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an importa ..."
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Cited by 11 (0 self)
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This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an important component of our world knowledge and that such knowledge is used in many different reasoning tasks. The work is further motivated by the observation that previous formalisms for representing probabilistic information are inadequate for representing statistical knowledge. The representation mechanism takes the form of a logic that is capable of representing a wide variety of statistical knowledge, and that possesses an intuitive formal semantics based on the simple notions of sets of objects and probabilities defined over those sets. Furthermore, a proof theory is developed and is shown to be sound and complete. The formalism offers a perspicuous and powerful representational tool for stat...
On sufficient conditions for unsatisfiability of random formulas
 JOURNAL OF THE ACM
, 2004
"... A descriptive complexity approach to random 3SAT is initiated. We show that unsatisfiability of any significant fraction of random 3CNF formulas cannot be certified by any property that is expressible in Datalog. Combined with the known relationship between the complexity of constraint satisfactio ..."
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Cited by 11 (2 self)
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A descriptive complexity approach to random 3SAT is initiated. We show that unsatisfiability of any significant fraction of random 3CNF formulas cannot be certified by any property that is expressible in Datalog. Combined with the known relationship between the complexity of constraint satisfaction problems and expressibility in Datalog, our result implies that any constraint propagation algorithm working with small constraints will fail to certify unsatisfiability almost always. Our result is a consequence of designing a winning strategy for one of the players in the existential pebble game. The winning strategy makes use of certain extension axioms that we introduce and hold almost surely on a random 3CNF formula. The second contribution of our work is the connection between finite model theory and propositional proof complexity. To make this connection explicit, we establish a tight relationship between the number of pebbles needed to win the game and the width of the Resolution refutations. As a consequence to our result and the known sizewidth relationship in Resolution, we obtain new proofs of the exponential lower bounds for Resolution refutations of random 3CNF formulas and the Pigeonhole Principle.