Gernot Salzer | Tu Wien (original) (raw)

Papers by Gernot Salzer

Logic Programming and Automated Reasoning, Jan 1, 1992

Abstract. In various fields using first order terms - like automated reason-ing, logic programmin... more Abstract. In various fields using first order terms - like automated reason-ing, logic programming or term rewriting - we encounter infinite sequences of structurally similar terms, leading to non-terminating or at least time and space consuming computations. As a remedy we ...

Automated Deduction—Cade-13, Jan 1, 1996

Abstract. We investigate the problem of finding optimal axiomatiza-tions for operators and distri... more Abstract. We investigate the problem of finding optimal axiomatiza-tions for operators and distribution quantifiers in finitely-valued first-order logics. We show that the problem can be viewed as the minimiza-tion of certain two-valued propositional formulas. We outline a general ...

Studia Logica, Jan 1, 1998

A general class of labeled sequent calculi is investigated, and necessary and su cient conditions... more A general class of labeled sequent calculi is investigated, and necessary and su cient conditions are given for when such a calculus is sound and complete for a nite-valued logic if the labels are interpreted as sets of truth values (sets-as-signs). Furthermore, it is shown that any nitevalued logic can be given an axiomatization by s u c h a labeled calculus using arbitrary \systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the number of truth values, and it is shown that this bound is tight.

Theoretical Computer …, Jan 1, 1996

The declarative semantics of nonmonotonic logic programming has largely been based on proposition... more The declarative semantics of nonmonotonic logic programming has largely been based on propositional programs. However, the ground instantiation of a logic program may be very large, and likewise, a ground stable model may also be very large. We develop a non-ground semantic theory for non-monotonic logic programming. Its principal advantage is that stable models and well-founded models can be represented as sets of atoms, rather than as sets of ground atoms. A set SI of atoms may be viewed as a compact representation of the Herbrand interpretation consisting of all ground instances of atoms in SI. We develop generalizations of the stable and well-founded semantics based on such non-ground interpretations SI. The key notions for our theory are those of covers and anticovers. A cover as well as its anticover are sets of substitutions non-ground in general -representing all substitutions obtained by ground instantiating some substitution in the (anti)cover, with the additional requirement that each ground substitution is represented either by the cover or by the anticover, but not by both. We develop methods for computing anticovers for a given cover, show that membership in so-called optimal covers is decidable, and investigate the complexity in the Datalog case.

Logic Programming and Automated Reasoning, Jan 1, 1993

Abstract. In recent years interesting decidability results for syntacti-cally specified classes o... more Abstract. In recent years interesting decidability results for syntacti-cally specified classes of clause sets have been achieved by employing resolution as a decision procedure. We extend this line of research by considering also clauses with equality literals. We use a special ...

Lecture Notes in Artificial Intelligence 1761 Subserks of Lecture Notes in Computer Science Ricar... more Lecture Notes in Artificial Intelligence 1761 Subserks of Lecture Notes in Computer Science Ricardo Caferra Gernot Salzer (Eds.) Automated Deduction in Classical and Non. Classical Logics Selected Papers Springer ... Lecture Notes in Artificial Intelligence 1761 Subseries of ...

Electronic Notes in Theoretical Computer Science, Jan 1, 2003

is the fourth in a series of workshops intended to focus effort on First-Order Theorem Proving as... more is the fourth in a series of workshops intended to focus effort on First-Order Theorem Proving as a core theme of Automated Deduction, and to provide a forum for presentation of recent work and discussion of research in progress. The previous workshops of this series were held at Schloss The technical program of FTP'2003 consists of three invited talks, twelve regular papers, two system descriptions and two position papers. The topics of these papers match very well those of the workshop which cover theorem proving in first-order classical, many-valued, modal and description logics, including nonexclusively: resolution, equational reasoning, term-rewriting, model construction, constraint reasoning, unification, description logics, propositional logic, specialized decision procedures; strategies and complexity of theorem proving procedures; implementation techniques and applications of first-order theorem provers to verification, artificial intelligence, mathematics and education. We sincerely thank everyone who contributed to make this workshop possible.

Theory of Computing …, Jan 1, 2008

We investigate the complexity of the satisfiability problem of constraints over finite totally or... more We investigate the complexity of the satisfiability problem of constraints over finite totally ordered domains. In our context, a clausal constraint is a disjunction of inequalities of the form x ≥ d and x ≤ d. We classify the complexity of constraints based on clausal patterns. A pattern abstracts away from variables and contains only information about the domain elements and the type of inequalities occurring in a constraint. Every finite set of patterns gives rise to a (clausal) constraint satisfaction problem in which all constraints in instances must have an allowed pattern. We prove that every such problem is either polynomially decidable or NPcomplete, and give a polynomial-time algorithm for recognizing the tractable cases. Some of these tractable cases are new and have not been previously identified in the literature. * The work has been supported byÉGIDE 06606ZF andÖAD Amadeus 18/2004. †

Automated Deduction—Cade-13, Jan 1, 1996

MUltlog is a system which takes as input the specification of a finitely-valued first-order logic... more MUltlog is a system which takes as input the specification of a finitely-valued first-order logic and produces a sequent calculus, a natural deduction system, and a calculus for transforming a many-valued formula to clauses suitable for many-valued resolution. All generated rules are optimized regarding their branching degree. The output is in the form of a scientific paper, written in LAT E X.

Developments in Theoretical Computer Science, Jan 1, 1994

Solvable Classes Of Cycle Unification Problems Gernot Salzer Abteilung fur Anwendvngen der formal... more Solvable Classes Of Cycle Unification Problems Gernot Salzer Abteilung fur Anwendvngen der formalen Logik, Instttut fur Computersprachen, Technische Universitat Wien, Karlsplatz 13/E185-2, A-1040 Wien/Austna; email: salzer «logic. tuwien. ac. at Abstract. In resolution ...

Rewriting Techniques and Applications, Jan 1, 2004

Automated Deduction—CADE-12, Jan 1, 1994

Abstract. In resolution theorem proving as well as in its descendant, logic programming, we are f... more Abstract. In resolution theorem proving as well as in its descendant, logic programming, we are frequently confronted with binary clauses causing lengthy or infinite computations because of their self-resolvents. In this paper we investigate unification modulo a binary clause, ...

Proceedings of the 2009 International …, Jan 1, 2009

Space-based computing middleware offers a data driven style for the coordination of processes. Th... more Space-based computing middleware offers a data driven style for the coordination of processes. The interaction requirements between these processes can be complex, and the template matching coordination law of the Linda and JavaSpaces model is not sufficient. Moreover, the usage should not be limited to a single platform. Several authors have proposed coordination extensions, but besides the suggestion to use XML or RDF based query facilities, a formalization of a general and extensible space-based coordination model has not yet been realized. In this paper we present the algebraic data structures and the coordination model based on a navigational query language for the extensible virtual shared memory architecture, and show how they can be adapted to support arbitrary coordination laws by the introduction of user-definable matchmaker and selector functions. The platform independence is achieved through a language independent communication protocol. The formal specification of the data model is the necessary basis for this protocol.

Information and Computation, Jan 1, 2000

We investigate the problem of finding optimal axiomatizations for operators and distribution quan... more We investigate the problem of finding optimal axiomatizations for operators and distribution quantifiers in finitely valued first-order logics. We show that the problem can be viewed as the minimization of certain propositional formulas. We outline a general procedure leading to optimized ...

Automated Reasoning, Jan 1, 2004

Given a finite set of vectors over a finite totally ordered domain, we study the problem of compu... more Given a finite set of vectors over a finite totally ordered domain, we study the problem of computing a constraint in conjunctive normal form such that the set of solutions for the produced constraint is identical to the original set. We develop an efficient polynomial-time algorithm for the general case, followed by specific polynomial-time algorithms producing Horn, dual Horn, and bijunctive constraints for sets of vectors closed under the operations of conjunction, disjunction, and median, respectively. We also consider the affine constraints, analyzing them by means of computer algebra. Our results generalize the work of Dechter and Pearl on relational data, as well as the papers by Hébrard and Zanuttini. They also complete the results of Hähnle et al. on multivalued logics and Jeavons et al. on the algebraic approach to constraints. We view our work as a step toward a complete complexity classification of constraint satisfaction problems over finite domains.

The Unified Modeling Language (UML) has become a universal tool for the formal object-oriented sp... more The Unified Modeling Language (UML) has become a universal tool for the formal object-oriented specification of hard-and software. In particular, UML class diagrams and so-called multiplicities, which restrict the number of links between objects, are essential when using ...

Mathematical Foundations of Computer Science …, Jan 1, 1998

We investigate the word and the subsumption problem for recurrent term schematizations, which are... more We investigate the word and the subsumption problem for recurrent term schematizations, which are a special type of constraints based on iteration. By means of uni cation, we reduce these problems to a fragment of Presburger arithmetic. Our approach is applicable to all recurrent term schematizations having a nitary uni cation algorithm. Furthermore, we study a particular form of the complement problem. Given a nite set of terms, we ask whether its complement can be nitely represented by schematizations, using only the equality predicate without negation. The answer is negative as there are ground terms too complex to be represented by schematizations with limited resources.

Logic Programming and Automated Reasoning, Jan 1, 1992

Abstract. In various fields using first order terms - like automated reason-ing, logic programmin... more Abstract. In various fields using first order terms - like automated reason-ing, logic programming or term rewriting - we encounter infinite sequences of structurally similar terms, leading to non-terminating or at least time and space consuming computations. As a remedy we ...

Automated Deduction—Cade-13, Jan 1, 1996

Abstract. We investigate the problem of finding optimal axiomatiza-tions for operators and distri... more Abstract. We investigate the problem of finding optimal axiomatiza-tions for operators and distribution quantifiers in finitely-valued first-order logics. We show that the problem can be viewed as the minimiza-tion of certain two-valued propositional formulas. We outline a general ...

Studia Logica, Jan 1, 1998

A general class of labeled sequent calculi is investigated, and necessary and su cient conditions... more A general class of labeled sequent calculi is investigated, and necessary and su cient conditions are given for when such a calculus is sound and complete for a nite-valued logic if the labels are interpreted as sets of truth values (sets-as-signs). Furthermore, it is shown that any nitevalued logic can be given an axiomatization by s u c h a labeled calculus using arbitrary \systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the number of truth values, and it is shown that this bound is tight.

Theoretical Computer …, Jan 1, 1996

The declarative semantics of nonmonotonic logic programming has largely been based on proposition... more The declarative semantics of nonmonotonic logic programming has largely been based on propositional programs. However, the ground instantiation of a logic program may be very large, and likewise, a ground stable model may also be very large. We develop a non-ground semantic theory for non-monotonic logic programming. Its principal advantage is that stable models and well-founded models can be represented as sets of atoms, rather than as sets of ground atoms. A set SI of atoms may be viewed as a compact representation of the Herbrand interpretation consisting of all ground instances of atoms in SI. We develop generalizations of the stable and well-founded semantics based on such non-ground interpretations SI. The key notions for our theory are those of covers and anticovers. A cover as well as its anticover are sets of substitutions non-ground in general -representing all substitutions obtained by ground instantiating some substitution in the (anti)cover, with the additional requirement that each ground substitution is represented either by the cover or by the anticover, but not by both. We develop methods for computing anticovers for a given cover, show that membership in so-called optimal covers is decidable, and investigate the complexity in the Datalog case.

Logic Programming and Automated Reasoning, Jan 1, 1993

Abstract. In recent years interesting decidability results for syntacti-cally specified classes o... more Abstract. In recent years interesting decidability results for syntacti-cally specified classes of clause sets have been achieved by employing resolution as a decision procedure. We extend this line of research by considering also clauses with equality literals. We use a special ...

Lecture Notes in Artificial Intelligence 1761 Subserks of Lecture Notes in Computer Science Ricar... more Lecture Notes in Artificial Intelligence 1761 Subserks of Lecture Notes in Computer Science Ricardo Caferra Gernot Salzer (Eds.) Automated Deduction in Classical and Non. Classical Logics Selected Papers Springer ... Lecture Notes in Artificial Intelligence 1761 Subseries of ...

Electronic Notes in Theoretical Computer Science, Jan 1, 2003

is the fourth in a series of workshops intended to focus effort on First-Order Theorem Proving as... more is the fourth in a series of workshops intended to focus effort on First-Order Theorem Proving as a core theme of Automated Deduction, and to provide a forum for presentation of recent work and discussion of research in progress. The previous workshops of this series were held at Schloss The technical program of FTP'2003 consists of three invited talks, twelve regular papers, two system descriptions and two position papers. The topics of these papers match very well those of the workshop which cover theorem proving in first-order classical, many-valued, modal and description logics, including nonexclusively: resolution, equational reasoning, term-rewriting, model construction, constraint reasoning, unification, description logics, propositional logic, specialized decision procedures; strategies and complexity of theorem proving procedures; implementation techniques and applications of first-order theorem provers to verification, artificial intelligence, mathematics and education. We sincerely thank everyone who contributed to make this workshop possible.

Theory of Computing …, Jan 1, 2008

We investigate the complexity of the satisfiability problem of constraints over finite totally or... more We investigate the complexity of the satisfiability problem of constraints over finite totally ordered domains. In our context, a clausal constraint is a disjunction of inequalities of the form x ≥ d and x ≤ d. We classify the complexity of constraints based on clausal patterns. A pattern abstracts away from variables and contains only information about the domain elements and the type of inequalities occurring in a constraint. Every finite set of patterns gives rise to a (clausal) constraint satisfaction problem in which all constraints in instances must have an allowed pattern. We prove that every such problem is either polynomially decidable or NPcomplete, and give a polynomial-time algorithm for recognizing the tractable cases. Some of these tractable cases are new and have not been previously identified in the literature. * The work has been supported byÉGIDE 06606ZF andÖAD Amadeus 18/2004. †

Automated Deduction—Cade-13, Jan 1, 1996

MUltlog is a system which takes as input the specification of a finitely-valued first-order logic... more MUltlog is a system which takes as input the specification of a finitely-valued first-order logic and produces a sequent calculus, a natural deduction system, and a calculus for transforming a many-valued formula to clauses suitable for many-valued resolution. All generated rules are optimized regarding their branching degree. The output is in the form of a scientific paper, written in LAT E X.

Developments in Theoretical Computer Science, Jan 1, 1994

Solvable Classes Of Cycle Unification Problems Gernot Salzer Abteilung fur Anwendvngen der formal... more Solvable Classes Of Cycle Unification Problems Gernot Salzer Abteilung fur Anwendvngen der formalen Logik, Instttut fur Computersprachen, Technische Universitat Wien, Karlsplatz 13/E185-2, A-1040 Wien/Austna; email: salzer «logic. tuwien. ac. at Abstract. In resolution ...

Rewriting Techniques and Applications, Jan 1, 2004

Automated Deduction—CADE-12, Jan 1, 1994

Abstract. In resolution theorem proving as well as in its descendant, logic programming, we are f... more Abstract. In resolution theorem proving as well as in its descendant, logic programming, we are frequently confronted with binary clauses causing lengthy or infinite computations because of their self-resolvents. In this paper we investigate unification modulo a binary clause, ...

Proceedings of the 2009 International …, Jan 1, 2009

Space-based computing middleware offers a data driven style for the coordination of processes. Th... more Space-based computing middleware offers a data driven style for the coordination of processes. The interaction requirements between these processes can be complex, and the template matching coordination law of the Linda and JavaSpaces model is not sufficient. Moreover, the usage should not be limited to a single platform. Several authors have proposed coordination extensions, but besides the suggestion to use XML or RDF based query facilities, a formalization of a general and extensible space-based coordination model has not yet been realized. In this paper we present the algebraic data structures and the coordination model based on a navigational query language for the extensible virtual shared memory architecture, and show how they can be adapted to support arbitrary coordination laws by the introduction of user-definable matchmaker and selector functions. The platform independence is achieved through a language independent communication protocol. The formal specification of the data model is the necessary basis for this protocol.

Information and Computation, Jan 1, 2000

We investigate the problem of finding optimal axiomatizations for operators and distribution quan... more We investigate the problem of finding optimal axiomatizations for operators and distribution quantifiers in finitely valued first-order logics. We show that the problem can be viewed as the minimization of certain propositional formulas. We outline a general procedure leading to optimized ...

Automated Reasoning, Jan 1, 2004

Given a finite set of vectors over a finite totally ordered domain, we study the problem of compu... more Given a finite set of vectors over a finite totally ordered domain, we study the problem of computing a constraint in conjunctive normal form such that the set of solutions for the produced constraint is identical to the original set. We develop an efficient polynomial-time algorithm for the general case, followed by specific polynomial-time algorithms producing Horn, dual Horn, and bijunctive constraints for sets of vectors closed under the operations of conjunction, disjunction, and median, respectively. We also consider the affine constraints, analyzing them by means of computer algebra. Our results generalize the work of Dechter and Pearl on relational data, as well as the papers by Hébrard and Zanuttini. They also complete the results of Hähnle et al. on multivalued logics and Jeavons et al. on the algebraic approach to constraints. We view our work as a step toward a complete complexity classification of constraint satisfaction problems over finite domains.

The Unified Modeling Language (UML) has become a universal tool for the formal object-oriented sp... more The Unified Modeling Language (UML) has become a universal tool for the formal object-oriented specification of hard-and software. In particular, UML class diagrams and so-called multiplicities, which restrict the number of links between objects, are essential when using ...

Mathematical Foundations of Computer Science …, Jan 1, 1998

We investigate the word and the subsumption problem for recurrent term schematizations, which are... more We investigate the word and the subsumption problem for recurrent term schematizations, which are a special type of constraints based on iteration. By means of uni cation, we reduce these problems to a fragment of Presburger arithmetic. Our approach is applicable to all recurrent term schematizations having a nitary uni cation algorithm. Furthermore, we study a particular form of the complement problem. Given a nite set of terms, we ask whether its complement can be nitely represented by schematizations, using only the equality predicate without negation. The answer is negative as there are ground terms too complex to be represented by schematizations with limited resources.