A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In KI 2001, Proceedings, volume 2174 of LNCS, pages 18--32. Springer, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....sets of (partial) types. A tableau calculus for temporal description logics with expanding domains is implemented in [32] Those algorithms are easily modi ed to obtain an algorithm deciding the future fragment of QTL(hN; i) QT L . The second approach employs the resolution method. [23] provides a clausal temporal resolution calculus which is complete for those formulas of the future fragment of QTL(hN; i) QT L 1 in which only is applied to open formulas (other temporal operators may be applied only to sentences) 9 Expressive completeness The temporal language QT L ....

A. Degtyarev and M. Fisher. Towards First-Order Temporal Resolution. In F. Baader, G. Brewka and T. Eiter, editors, KI 2001: Advances in Arti cial Intelligence, volume 2174 of LNCS, pages 18-32. Springer, 2001.

....and other fields. For example, many temporal description logics and spatio temporal logics can be regarded as fragments of monodic FOTL [11, 6, 22] Unfortunately, the decision procedures provided in [10] are of model theoretic character and cannot be used as a basis for implementations. In [1] a resolution based approach was developed for certain subfragments of the monodic fragment. A tableau based analysis of the decision problem for monodic FOTL has been missing. In this paper we are trying to fill in this gap. More specifically, our aims are as follows: 1. to develop a general ....

A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In F. Baader, G. Brewka, and T. Eiter, editors, Advances in Artificial Intelligence (KI'2001.

....sets of (partial) types. A tableau calculus for temporal description logics with expanding domains is implemented in [32] Those algorithms are easily modi ed to obtain an algorithm deciding the future fragment of QTL(hN; i) QT L 1 . The second approach employs the resolution method. [23] provides a clausal temporal resolution calculus which is complete for those formulas of the future fragment of QTL(hN; i) QT L 1 in which only is applied to open formulas (other temporal operators may be applied only to sentences) 9 Expressive completeness The temporal language QT L ....

A. Degtyarev and M. Fisher. Towards First-Order Temporal Resolution. In F. Baader, G. Brewka and T. Eiter, editors, KI

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A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In KI 2001, Proceedings, volume 2174 of LNCS, pages 18--32. Springer, 2001.

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A. Degtyarev, M. Fisher, Towards first-order temporal resolution, in: Proc. KI 2001.

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A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In KI 2001, Proceedings, volume 2174 of Lecture Notes in Computer Science, pages 18--32. Springer, 2001.

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A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In KI 2001.

....has led to considerable research activity examining the monodic fragment, in terms of decidable classes, extensions, applications and mechanisation, etc. Concerning the mechanisation of monodic temporal logics, general tableau and resolution calculi have already been defined, in [13] and [5, 3], respectively. However, neither of these is particularly practical: the tableau method requires representation of all possible first order models, while the resolution method requires the maximal combination of all temporal clauses. In this paper, we focus on an important subclass of temporal ....

A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In KI 2001.

.... yield a tableau based procedure for decidable monodic fragments, and a number of its instantiations, has been presented in [10] In this paper, we provide a complete resolution calculus for monodic first order temporal logic, based on our work on clausal temporal resolution over a number of years [5, 7, 1, 2]. The structure of the paper is as follows. After a brief introduction into first order temporal logic, we show that any monodic temporal problem can be transformed into a normal form (Section 3) and present the temporal resolution calculus (Section 4) The main focus, within this paper, is on ....

....3 Divided Separated Normal Form Definition 1 (Temporal Step Clauses) A temporal step clause is a formula either in the form p ) l, where p is a proposition and l is a propositional literal, or 8x(P(x) W.r.t. satisfiability, other temporal operators can be represented using these operators [6, 1]. M(x) where P is a unary predicate and M is a unary literal. We call a clause of the the first type an (original) ground step clause, and of the second type an (original) non ground step clause. Definition 2 (Monodic Temporal Specification) A Monodic Temporal Specification, SP, is a triple ....

[Article contains additional citation context not shown here]

A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In KI 2001, Proceedings, volume 2174 of Lecture Notes in Computer Science, pages 18--32. Springer, 2001. 19

.... The addition of either equality or function symbols to monodic FOLTL leads to the loss of recursive enumerability [16, 4] The only known decidable monodic fragment with equality (but without functional symbols) termed monodic packed fragment, was established in [12] In previous work [2, 3], we have extended the clausal temporal resolution approach [8] to the monodic fragment of FOLTL. While this is useful as a practical proof technique for certain monodic classes, in this paper we show that the use of clausal temporal resolution provides us with increased understanding of the ....

.... a renaming technique replacing non atomic subformulae with new predicates and removing all occurrences of the U operator [6, 3] The result is a quadruple , U,S , E# With respect to satisfiability, other temporal operators, U (until) and W (weak until) can be represented using these operators [7, 2]. where I and U are an initial part and a universal part, respectively, given by sets of arbitrary closed first order formulae; S is a step part given by a set of step clauses (or step rules) M(x) a non ground step clause) p m (a ground step clause) and E is an eventuality part given ....

A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In Proc. KI 2001, volume 2174 of Lecture Notes in Computer Science, pages 18--32. Springer, 2001.

.... of this, the addition of equality or function symbols leads to the loss of recursive enumerability [15, 4] In [3] we presented a resolution procedure for the monodic fragment with interpretations over constant domains, based on our work on clausal temporal resolution over a number of years [6, 8, 1, 2]. In this paper, we provide a complete resolution calculus for monodic first order temporal logic over expanding domains. The beauty of the result is that we could use exactly the same machinary, by restricting the form of merged clauses. The structure of the paper is as follows. After a brief ....

....It can be readily checked that this algorithm can be also employed in the expanding domain case. 5 Completeness of Monodic Resolution Over Expanding Domains In order to prove completeness of the temporal resolution method, we introduce additional concepts (some of which were already defined in [1]) Let P = hU ; I ; S i [E be an unconditional eventuality monodic temporal problem. Let fP ; P N g and fp 1 ; p n g, N;n 0, be the sets of all (monadic) predicate symbols and all propositional symbols, respectively, occurring in S [ E . Let D be the set of all mappings from ....

[Article contains additional citation context not shown here]

A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In KI 2001, Proceedings, volume 2174 of Lecture Notes in Computer Science, pages 18--32. Springer, 2001.

....has led to considerable research activity examining the monodic fragment, in terms of decidable classes, extensions, applications and mechanisation, etc. Concerning the mechanisation of monodic temporal logics, general tableau and resolution calculi have already been defined, in [12] and [4, 3], respectively. However, neither of these is particularly practical: the tableau method requires representation of all possible first order models, while the resolution method requires the maximal combination of all temporal clauses. In this paper, we focus on an important subclass of temporal ....

A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In KI 2001.

....cases. The simplified clausal resolution procedure is given in x3 and x5. The case of one eventuality is considered in x6. The results of these sections refine those given in [3] an extension of the simplified resolution calculus to fragments of first order temporal logic has been considered in [4, 5]. 2 Preliminaries We define the temporal logic we use based on the following symbols: atomic propositions P rop = a; b; c : p; q; r : Boolean operators : true ( true ) false ( false ) temporal operators start ( at the initial moment of time ) always in the ....

A. Degtyarev and M.Fisher. Towards First-Order Temporal Resolution. In Proc. KI 2001, volume 2174 of LNCS. Springer Verlag, 2001.

....The simpli ed clausal resolution procedure is given in sections 3 and 5. The case of one eventuality is considered in section 6. The results of these sections re ne those given in [3] An extension of the simpli ed resolution calculus to fragments of rst order temporal logic we considered in [4, 5]. 2 Preliminaries We de ne the temporal logic we use based on the following symbols: atomic propositions P rop = a; b; c : p; q; r : Boolean operators : true ( true ) false ( false ) temporal operators start ( at the initial moment of time ) always in the ....

A. Degtyarev and M.Fisher. Towards First-Order Temporal Resolution. In F. Baader, G. Brewka and T. Eiter, editors, Proceedings of KI 2001: Advances in Arti cial Intelligence, volume 2174 of Lecture Notes in Computer Science, pages 18-32. Springer Verlag, September 2001.

....both sequents lie outside of any known complete fragment of FOLTL. Recently, the interesting monodic fragment of first order temporal logic has been investigated [HWZ00] which has a quite transparent (and intuitive) syntactic definition and a finite Hilbert like inference system [WZ01] In [DF01] a clausal temporal resolution procedure has been developed covering a special subclass of the monodic fragment, namely the subclass of ground eventuality monodic problems. In this paper we apply the clausal resolution method in order to give a sound and complete scheme for searching for ....

....can automate its proof, using our invariant scheme. This aspect is demonstrated in examples. Structure of the paper. We split our presentation into two main parts: the first essentially concerns propositional temporal logic; the second targets a fragment of monodic first order temporal logic [HWZ00, DF01]. While the propositional part is clearly included within the first order part, we have chosen to introduce this separately in order to give the reader a simpler introduction to the techniques involved. Thus, in x3, we consider this propositional temporal fragment, providing formal justification ....

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A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In Proccedings of KI-2001, volume 2174 of LNAI, 2001.

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A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In Proccedings of KI-2001, volume 2174 of LNAI, 2001.

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