Burckert, H. J., "A Resolution Principle for a Logic With Restricted Quantifiers," Lecture Notes in Artificial Intelligence, Vol. 568, Springer-Verlag, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....axioms are included. In order for a system including separated versions of these rules to be complete, a number of additional types of axioms must be added such as separated versions of predicate congruence axioms. Further discussion of completeness is outside the scope of this paper. Burckert 91] points out that for some restriction theories, closed separated refutations can always be obtained by considering the validity of only the restrictions of individual clauses. For instance, it is proven that if T is a definite theory, i.e. a theory that can be written as a set of definite ....

Burckert, H. J., "A Resolution Principle for a Logic With Restricted Quantifiers," Lecture Notes in Artificial Intelligence, Vol. 568, Springer-Verlag, 1991.

....positive literals in the conjunction and then the formula is satis able just in case the graph does not contain a positive occurrence of one of the negative literals in the conjunction. Decision procedures are interfaced to SNARK through separated inference rules which are based on RQ resolution [2]. They work with clauses that are separated relative to a subtheory. De nition (Separated Clause) Let L be the language of a theory T , a sorted rst order theory with equality. We treat equality as a logical symbol, so =62 L. Let L 1 L be the language of T 1 T . A clause C with the ....

H. J. Burckert, \A Resolution Principle for a Logic With Restricted Quanti ers," Lecture Notes in Arti cial Intelligence, Vol. 568, Springer-Verlag, 1991.

....accomplished by extending each inference rule in a uniform manner. This paper only discusses separated binar T resolution and separated paramodulation, but the other rules are extended similarly. Separated binar T resolution is similar to resolution with restricted quantifiers or RQ resolution [3]. Recall that, given a first order theory T and a first order formula q, we prove q=qby refutation by showing that T LJ is unsatisfiable. Assuming that Tis satisfiable, this amounts to showing that no model of Tis a model of q. The general idea of our binar T resolution rule (as well as ....

....of these rules to be complete, separated versions of congruence axioms for some theory predicate and function symbols are added. An example of a predicate congruence axiom is (x = y) P(x) P(y) Space does not permit a proof of the completeness of separated resolution and paramodulation here. [3] points out that for some restriction theories, closed separated refutations can always be obtained by considering the entailment of the restrictions of only individual clauses. For instance, it is proven that if T 1 is a definite theory, i.e. a theory that can be written as a set of definite ....

Burckert, H. J., "A Resolution Principle for a Logic With Restricted Quantifiers," Lecture Notes in Artificial Intelligence, Vol. 568, Springer-Verlag, 1991.

....special purpose reasoner can significantly improve the speed of inference, but a suitable interface to the general purpose inference procedure must be designed. Snark supports a time and date procedure with an interface to the ordinary resolution rule, based on the constraint resolution framework [Burckert]. The snark temporal reasoning facility is switched on by selecting the option use temporal reasoning, e.g. by evaluating (default use temporal reasoning) 6 TEMPORAL REASONING 62 before initialization; henceforth, in this section, we assume that the facility has been turned on. When using ....

....For instance, even if we assert (before the civil war the age of aquarius) snark will not know that (before (day fn 1 the civil war) day fn 2 the age of aquarius) 6. 9 Temporal Reasoner Interface The interface between snark and the Allen temporal reasoning procedure uses constraint resolution [Burckert]. Each row is split between ; If a pure temporal relation between two ground (i.e. variable less) terms is asserted or deduced, it is introduced into a graph representation of all known temporal relations. If the relation already follows from the relations in the graph, the graph is not ....

H.-J. Burckert, A Resolution Principle for a Logic with Restricted Quantifiers, Lecture Notes in Artificial Intelligence No. 568, Springer Verlag, Berlin (1991).

....including separated versions of these rules to be complete, a number of additional types of axioms must be added such as separated versions of predicate congruence axioms. In practice, completeness has not been an issue in our work on deductive synthesis, so we do not discuss it further here. Burckert 91] points out that for some restriction theories, closed separated refutations can always be obtained by considering the validity of only the restrictions of individual clauses. For instance, it is proven that if T 1 is a definite theory, i.e. a theory that can be written as a set of definite ....

Burckert, H. J., "A Resolution Principle for a Logic With Restricted Quantifiers," Lecture Notes in Artificial Intelligence, Vol. 568, Springer-Verlag, 1991.

....special purpose reasoner can significantly improve the speed of inference, but a suitable interface to the general purpose inference procedure must be designed. Snark supports a time and date procedure with an interface to the ordinary resolution rule, based on the constraint resolution framework [Burckert]. The snark temporal reasoning facility is switched on by selecting the option use temporal reasoning, e.g. by evaluating (default use temporal reasoning) 6 TEMPORAL REASONING 62 before initialization; henceforth, in this section, we assume that the facility has been turned on. When using ....

....For instance, even if we assert (before the civil war the age of aquarius) snark will not know that (before (day fn 1 the civil war) day fn 2 the age of aquarius) 6. 9 Temporal Reasoner Interface The interface between snark and the Allen temporal reasoning procedure uses constraint resolution [Burckert]. Each row is split between ; If a pure temporal relation between two ground (i.e. variable less) terms is asserted or deduced, it is introduced into a graph representation of all known temporal relations. If the relation already follows from the relations in the graph, the graph is not ....

H.-J. Burckert, A Resolution Principle for a Logic with Restricted Quantifiers, Lecture Notes in Artificial Intelligence No. 568, Springer Verlag, Berlin (1991).

....is AC ; a clause will be generated for each most general AC unifier, but there are 34359607 481 of them. Using an AC unification constraint, only one clause is deduced : P (x) j[ x x x x=AC y 1 y 2 y 3 y 4 ]j . The advantage of such constraints was already pointed out in [KK89, KKR90] and in [Bur91]. The main result of this paper is the definition of a refutationally complete set of inference rules, compatible with simplification, for deduction with constraints in AC theories. These inference rules are non trivial refinements of rules defined in [RV93] by including constraints of ffl ....

H.-J. Burckert. A Resolution Principle for a Logic with Restricted Quantifiers, volume 568 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 1991.

....a generic institution (logical system) for ECLP with properties close to the institutions used in algebraic specification, to prove a general Herbrand Theorem for ECLP (novel result to our knowledge) etc. On the practical side, the above results open the door for: with restricted quantifiers of [4] comes close to being a particular case of ECLP in that it uses extensions of some built in signature for defining its syntax and expansions of built in models for semantics. Direct transfer of software engineering techniques and methodologies developed by the algebraic specification community ....

H.-J. Burckert. A Resolution Principle for a Logic with Restricted Quantifiers, volume 568 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 1991.

....was supported by the EC Working Group CCL, EP6028. the term unification algorithm referred to an algorithm that computes a complete set of unifiers (see [SS89, Bou93] for the most recent results on combining such algorithms) With the development of constraint approaches to theorem proving [Bur91, NiR94] and term rewriting [KK89] the role of algorithms that compute complete sets of unifiers is more and more taken on by algorithms that decide solvability of the unification problems. In this setting, more general constraints than the equational constraints s = t of unification problems become ....

H.-J. Burckert. A Resolution Principle for a Logic with Restricted Quantifiers, LNCS 568, 1991.

....completion procedures to avoid non termination of the rewrite systems under consideration [JK86, Bac91] In both cases, the term unification algorithm refers to an algorithm that computes a complete set of unifiers. With the more recent development of constraint approaches to theorem proving [Bur91] and term rewriting [KK89] the role of algorithms that compute complete sets of unifiers is more and more taken on by algorithms that decide solvability of the unification problems. In this setting, more general constraints than the equational constraints s = t of unification problems become ....

H.-J. Burckert. A Resolution Principle for a Logic with Restricted Quantifiers, volume 568 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 1991.

....define the following set theoretic operations: a) subset(S1,S2) Gamma (8 X 2 S1) X 2 S2) b) disj(S1,S2) Gamma (8 X 2 S1) 8 Y 2 S2) X 6= Y) where predicate subset tests whether S1 is a subset of S2 and predicate disj tests whether S1 and S2 are disjoint sets. One might proceed as in [33, 9], by enhancing resolution to deal directly with RUQs. However, both for conceptual simplicity and for soundness concerns we prefer to transform extended Horn clauses into equivalent flogg clauses without RUQs (hints about a similar idea can be found in [32] We have proved that such a ....

Burckert, H.-J., A Resolution Principle for a Logic with Restricted Quantifiers. Springer-Verlag, New York, 1991.

....can be expected from the application of specialized techniques for automated theorem proving in first order theories. The general framework we refer to is the so called theory reasoning originally proposed by Stickel [16] and widely studied in the Artificial Intelligence community, e.g. [1, 2]. We focus on T theorem proving, a specific technique for automated theorem proving in a first order theory T proposed in [15] In [8] we deal with the problem of pairing the 2 as Pow translation with the T theorem proving technique for supporting automated theorem proving in modal logic. The ....

H.J. Burckert, A Resolution Principle for a Logic with Restricted Quantifier; Springer Verlag LNAI, 568, 1991.

....control set. As a matter of fact, we can have two extreme cases of ccts where at least two of the above connections are realised implicitly: 1. The signatures of the constraints and the kernels could be disjoint. By that we have modelled the resolution with restricted quantifiers of H.J. Burckert [4] The only difference is that we interpret his constraint theory in a different, non monotonic, way as our control set. He infers an empty clause, which has to have a constraint that is valid in the constraint theory, whereas we only demand the satisfiability of this constraint. By that we are able ....

Burckert, H.-J. (1991) A Resolution Principle for a Logic with Restricted Quantifiers, Lecture Notes in Artificial Intelligence 568 (Springer).

....center column of Table 1 because (a b) and (b a) is unsatisfiable in the background theory of . In practice, a special procedure would be invoked to identify the unsatisfiable conjunction of literals. In RQ resolution (also called constrained resolution) a clause is written as an implication [Burckert 91] The antecedent is called the constraints (or restrictions) Recall that for arbitrary first order formulas and , the clause is equivalent to the formula . For RQ reso Table 1: Resolution, Theory Resolution, and RQ Resolution Resolution Theory Resolution RQ Resolution parent parent resolvent ....

H. J. Burckert, "A Resolution Principle for a Logic With Restricted Quantifiers," Lecture Notes in Artificial Intelligence, Vol. 568, Springer-Verlag, 1991.

....algorithm referred to an algorithm that computes a complete set of unifiers (see [SS89, Bou90] for the most recent results on combining such algorithms) With the development of constraint approaches This author was supported by the EC Working Group CCL, EP6028. to theorem proving [Bur91] and term rewriting [KK89] the role of algorithms that compute complete sets of unifiers is more and more taken on by algorithms that decide solvability of the unification problems. In this setting, more general constraints than the equational constraints s = t of unification problems become ....

H.-J. Burckert. A Resolution Principle for a Logic with Restricted Quantifiers, LNCS 568, 1991.

....and efficient tools at each level. When, for instance for syntactic reasons, these two levels do not interfere, this idea leads to an interesting modularization of provers. This is a case similar to the CLP framework which has been studied in the context of knowledge representation for instance by [7, 15]. But we are interested here in using formulas defined with the equality predicate (possibly among others) at both levels. This induces an additional difficulty and we focus here on this kind of problem. A first motivation for introducing constraints in equational deduction processes arises when ....

H.-J. Burckert. A Resolution Principle for a Logic with Restricted Quantifiers, volume 568 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 1991.

....such that it needs only polynomial space. 5 Conclusion Decision procedures for unification rather than algorithms computing complete sets of unifiers or most general unifiers are, for example, of interest in constraintbased approaches to theorem proving, term rewriting, and logic programming [4, 15, 10, 9]. In this research note we have determined the exact complexity of the decision problem for Boolean unification. Whereas elementary unification is on the first level of the polynomial hierarchy (NP complete) unification with constants is on the second level ( Pi p 2 complete) and unification ....

H.-J. Burckert. A Resolution Principle for a Logic with Restricted Quantifiers, volume 568 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 1991.

....(CLP) is an elegant generalization of logic programming where the basic operation of logic programming, the unification, is replaced by the more general concept of constraint solving over a computation domain. The general scheme CLP(D) of constraint logic programming was developed in [9] In [3] a predicate logic with restricted quantifiers is discussed and a resolution principle for clauses with constraints was proposed, where unification is replaced by testing constraints for satisfiability over a restriction theory. Furthermore, in this book, a sort theory is also mentioned as an ....

....A derivation sequence is a possibly infinite sequence of goals connected by derivation steps. A derivation sequence is called succesful if it is finite and its last goal contains only constraints. This rule of inference is a special case of the resolution with restricted quantifiers described in [3]. Thus soundness and completeness of our system follow from the results presented in this book. The strategy of deduction can be modified for reasons of efficiency. In every derivation step the constraints C can be replaced by simplified constraints C s , if H j= C C s . The complete test for ....

H.-J. Burckert. A Resolution Principle for a Logic with Restricted Quantifiers, volume 568 of Lecture Notes in Artificial Intelligence. Springer-Verlag, Berlin, Heidelberg, 1991.

....been accomplished by extending each inference rule in a uniform manner. This paper only discusses separated binary resolution and separated paramodulation, but the other rules are extended similarly. Separated binary resolution is similar to resolution with restricted quantifiers or RQ resolution [3]. Recall that, given a first order theory T and a first order formula F, we prove T =F by refutation by showing that is unsatisfiable. Assuming that T is satisfiable, this amounts to showing that no model of T is a model of F. The general idea of our binary resolution rule (as well as ....

....separated versions of these rules to be complete, separated versions of congruence axioms for some theory predicate and function symbols are added. An example of a predicate congruence axiom is . Space does not permit a proof of the completeness of separated resolution and paramodulation here. [3] points out that for some restriction theories, closed separated refutations can always be obtained by considering the entailment of the restrictions of only individual clauses. For instance, it is proven that if T 1 is a definite theory, i.e. a theory that can be written as a set of definite ....

Burckert, H. J., "A Resolution Principle for a Logic With Restricted Quantifiers," Lecture Notes in Artificial Intelligence, Vol. 568, Springer-Verlag, 1991.

....1989, Smolka, 1989, Colmerauer, 1990] See also the chapters on Constraint Logic Programming in the Logic Programming volume of this handbook. The most general version of constrained resolution, which is independent of special applications like logic programming, has been defined by Burckert [Burckert, 1991]. The basic idea of this version comes from the observation that it is actually not necessary to unify the two resolution literals in a resolution step. It suffices to check whether the resolution literals are unifiable without computing the unifiers explicitly. Thus, the generation of resolvents ....

....If the constraints of an empty clause are satisfiable in all these models, the empty clause represents a contradiction as before. Otherwise we may have to derive several, but finitely many, empty clauses, such that the disjunction of their constraints is a tautology in the constraint theory [Burckert, 1991]. Speaking in terms of theory resolution, a constrained resolution refutation consists of a sequence of either standard resolution steps or, when the constraints are simplified, partial theory resolution steps where the simplified constraints form the (negated) residue, followed by a total theory ....

Burckert, H.-J. (1991). A Resolution Principle for a Logic with Restricted Quantifiers. Lecture Notes in Artificial Intelligence. Springer-Verlag, Berlin, Heidelberg, New York. to appear.

....problem description is encoded in first order formulas. Such constraint theories can be given by, e.g. sort hierarchies, feature logics, or terminological logics. Building upon this, constrained resolution allows one to integrate specific inference algorithms into the resolution principle ([3], 4] 10] 9] In logics with restricted quantifiers first order logics and constraint theory are connected by extending the classical quantifiers as follows. If Gamma is a (unary) constraint, i.e. an open formula over the signature of the constraint theory, formulas 8x: Gamma F and ....

....of the unfolding RQ formulas can directly be translated into a set of constrained clauses but not vice versa. 2 Since we are interested in using concepts as constraints we do not consider the general case where quantifiers can be indexed by a set of variables together with a constraint (cf. [3]) Knowledge Representation 407 H. J. Burckert and B. Hollunder and A. Laux If the kernel of a constrained clause is empty we call it an empty constrained clause, written as 2 jj Gamma. To check satisfiability of a set of constrained clauses the so called constrained resolution principle has ....

[Article contains additional citation context not shown here]

H.-J. Burckert, A Resolution Principle for a Logic with Restricted Quantifiers, volume 568 of LNAI, Springer, 1991.

No context found.

Burckert, H. J., "A Resolution Principle for a Logic With Restricted Quantifiers," Lecture Notes in Artificial Intelligence, Vol. 568, Springer-Verlag, 1991.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC