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Unification with Sequence Variables And Flexible Arity Symbols and its Extension with PatternTerms
 ARTIFICIAL INTELLIGENCE, AUTOMATED REASONING AND SYMBOLIC COMPUTATION. PROC. OF JOINT AISC’2002 – CALCULEMUS’2002 CONFERENCE, VOLUME 2385 OF LNAI
, 2002
"... A minimal and complete unification procedure for a theory with individual and sequence variables, free constants and free fixed and flexible arity function symbols is described and a brief overview of an extension with patternterms is given. ..."
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Cited by 27 (14 self)
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A minimal and complete unification procedure for a theory with individual and sequence variables, free constants and free fixed and flexible arity function symbols is described and a brief overview of an extension with patternterms is given.
Decision procedures for algebraic data types with abstractions
 IN 37TH ACM SIGACTSIGPLAN SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES (POPL), 2010. DECISION PROCEDURES FOR ORDERED COLLECTIONS 15 SHE75. SAHARON SHELAH. THE MONADIC THEORY OF ORDER. THA ANNALS OF MATHEMATICS OF MATHEMATICS
, 2010
"... We describe a family of decision procedures that extend the decision procedure for quantifierfree constraints on recursive algebraic data types (term algebras) to support recursive abstraction functions. Our abstraction functions are catamorphisms (term algebra homomorphisms) mapping algebraic data ..."
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Cited by 23 (11 self)
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We describe a family of decision procedures that extend the decision procedure for quantifierfree constraints on recursive algebraic data types (term algebras) to support recursive abstraction functions. Our abstraction functions are catamorphisms (term algebra homomorphisms) mapping algebraic data type values into values in other decidable theories (e.g. sets, multisets, lists, integers, booleans). Each instance of our decision procedure family is sound; we identify a widely applicable manytoone condition on abstraction functions that implies the completeness. Complete instances of our decision procedure include the following correctness statements: 1) a functional data structure implementation satisfies a recursively specified invariant, 2) such data structure conforms to a contract given in terms of sets, multisets, lists, sizes, or heights, 3) a transformation of a formula (or lambda term) abstract syntax tree changes the set of free variables in the specified way.
Induction and coinduction in sequent calculus
 Postproceedings of TYPES 2003, number 3085 in LNCS
, 2003
"... Abstract. Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and coinduction. These proof principles are based on a proof theoretic (rather than sett ..."
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Cited by 23 (8 self)
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Abstract. Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and coinduction. These proof principles are based on a proof theoretic (rather than settheoretic) notion of definition [13, 20, 25, 51]. Definitions are akin to (stratified) logic programs, where the left and right rules for defined atoms allow one to view theories as “closed ” or defining fixed points. The use of definitions makes it possible to reason intensionally about syntax, in particular enforcing free equality via unification. We add in a consistent way rules for pre and post fixed points, thus allowing the user to reason inductively and coinductively about properties of computational system making full use of higherorder abstract syntax. Consistency is guaranteed via cutelimination, where we give the first, to our knowledge, cutelimination procedure in the presence of general inductive and coinductive definitions. 1
A Comparison of Query Rewriting Techniques for DLLite
"... An incomplete database is defined by a set of constraints and a partial database instance [1]. Answering conjunctive queries over incomplete databases is an important computational task that lies at the core of many problems, such as information integration [12], data exchange [9], and data warehous ..."
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Cited by 22 (0 self)
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An incomplete database is defined by a set of constraints and a partial database instance [1]. Answering conjunctive queries over incomplete databases is an important computational task that lies at the core of many problems, such as information integration [12], data exchange [9], and data warehousing [17]. Given
A RewritingBased Inference System for the NRL Protocol Analyzer and its MetaLogical Properties
, 2005
"... The NRL Protocol Analyzer (NPA) is a tool for the formal specification and analysis of cryptographic protocols that has been used with great effect on a number of complex reallife protocols. One of the most interesting of its features is that it can be used to reason about security in face of attem ..."
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Cited by 22 (14 self)
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The NRL Protocol Analyzer (NPA) is a tool for the formal specification and analysis of cryptographic protocols that has been used with great effect on a number of complex reallife protocols. One of the most interesting of its features is that it can be used to reason about security in face of attempted attacks on lowlevel algebraic properties of the functions used in a protocol. Indeed, it has been used successfully to either reproduce or discover a number of such attacks. In this paper we give for the first time a precise formal specification of the main features of the NPA inference system: its grammarbased techniques for invariant generation and its backwards reachability analysis method. This formal specification is given within the wellknown rewriting framework so that the inference system is specified as a set of rewrite rules modulo an equational theory describing the behavior of the cryptographic algorithms involved. We then use this formalization to prove some important metalogical properties about the NPA inference system, including the soundness and completeness of the search algorithm and soundness of the grammar generation algorithm. The formalization and soundness and completeness theorems not only provide also a better understanding of the NPA as it currently operates, but provide a modular basis which can be used as a starting point for increasing the types of equational theories it can handle.
Explicit and Implicit Indeterminism: Reasoning About Uncertain and Contradictory Specifications of Dynamic Systems
 Journal of Logic Programming
, 1997
"... A highlevel action semantics to specify and reason about dynamic systems is presented which supports both uncertain knowledge (taken as explicit indeterminism) and contradictory information (taken as implicit indeterminism). We start by developing an action description language for intentionally re ..."
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Cited by 21 (12 self)
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A highlevel action semantics to specify and reason about dynamic systems is presented which supports both uncertain knowledge (taken as explicit indeterminism) and contradictory information (taken as implicit indeterminism). We start by developing an action description language for intentionally representing nondeterministic actions in dynamic systems. We then study the different possibilities of interpreting contradictory specifications of concurrent actions. We argue that the most reasonable interpretation which allows for exploiting as much information as possible is to take such conflicts as implicit indeterminism. As the second major contribution, we present a calculus for our resulting action semantics based on the logic programming paradigm including negationasfailure and equational theories. Soundness and completeness of this encoding wrt the notion of entailment in our highlevel action language is proved by taking the completion semantics for equational logic programs with...
Word Unification and Transformation of Generalized Equations
 Journal of Automated Reasoning
, 1993
"... Makanin's algorithm [Ma77] shows that it is decidable whether a word equation has a solution. The original description was hard to understand and not designed for implementation. Since words represent a fundamental data type, various authors have given improved descriptions [P'e81, Ab87, Sc90, Ja90] ..."
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Cited by 21 (1 self)
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Makanin's algorithm [Ma77] shows that it is decidable whether a word equation has a solution. The original description was hard to understand and not designed for implementation. Since words represent a fundamental data type, various authors have given improved descriptions [P'e81, Ab87, Sc90, Ja90]. In this paper we present a version of the algorithm which probably cannot be further simplified without fundamentally new insights which exceed Makanin's original ideas. We give a transformation which is efficient, conceptually simple and applies to arbitrary generalized equations. No further subprocedure is needed for the generation of the search tree. Particular attention is then given to the proof that proper generalized equations are transformed into proper generalized equations. This point, which is important for the termination argument, was treated erroneously in other papers. We also show that a combination of the basic algorithm for stringunification (see [Pl72, Le72, Si75, Si78]...
Matching in Description Logics with Existential Restrictions
 In Proc. of KR2000
, 2000
"... Matching of concepts against patterns is a new inference task in Description Logics, which was originally motivated by applications of the Classic system. Consequently, the work on this problem was until now mostly concerned with sublanguages of the Classic language, which does not allow for existen ..."
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Cited by 21 (14 self)
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Matching of concepts against patterns is a new inference task in Description Logics, which was originally motivated by applications of the Classic system. Consequently, the work on this problem was until now mostly concerned with sublanguages of the Classic language, which does not allow for existential restrictions. This paper extends the existing work on matching in two directions. On the one hand, the question of what are the most "interesting " solutions of matching problems is explored in more detail. On the other hand, for languages with existential restrictions both, the complexity of deciding the solvability of matching problems and the complexity of actually computing sets of "interesting " matchers are determined. The results show that existential restrictions make these computational tasks more complex. Whereas for sublanguages of Classic both problems could be solved in polynomial time, this is no longer possible for languages with existential restrictions.
Efficient Query Answering for OWL 2
"... Abstract. The QL profile of OWL 2 has been designed so that it is possible to use database technology for query answering via query rewriting. We present a comparison of our resolution based rewriting algorithm with the standard algorithm proposed by Calvanese et al., implementing both and conductin ..."
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Cited by 21 (4 self)
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Abstract. The QL profile of OWL 2 has been designed so that it is possible to use database technology for query answering via query rewriting. We present a comparison of our resolution based rewriting algorithm with the standard algorithm proposed by Calvanese et al., implementing both and conducting an empirical evaluation using ontologies and queries derived from realistic applications. The results indicate that our algorithm produces significantly smaller rewritings in most cases, which could be important for practicality in realistic applications. 1
An Algebraic Approach to Sharing Analysis of Logic Programs
 Journal of Logic Programming
, 1997
"... This paper describes an algebraic approach to the sharing analysis of logic programs based on an abstract domain of set logic programs. Set logic programs are logic programs in which the terms are sets of variables and unification is based on an associative, commutative, and idempotent equality theo ..."
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Cited by 20 (7 self)
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This paper describes an algebraic approach to the sharing analysis of logic programs based on an abstract domain of set logic programs. Set logic programs are logic programs in which the terms are sets of variables and unification is based on an associative, commutative, and idempotent equality theory. All of the basic operations required for sharing analyses, as well as their formal justification, are based on simple algebraic properties of set substitutions and setbased atoms. An ordering on setbased syntactic objects, similar to "less general" on concrete syntactic objects, is shown to reflect the notion of "less sharing" information. The (abstract) unification of a pair of setbased terms corresponds to finding their most general ACI1 unifier with respect to this ordering. The unification of a set of equations between setbased terms is defined exactly as in the concrete case, by solving the equations one by one and repeatedly applying their solutions to the remaini...