Apt, K.R. and M. Bezem (1990). Acyclic Programs. In: 7th International Conference on Logic Programming. MIT Press. Jerusalem, Israel.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....language, resp. union of regular pattern language, regular language, context free language) is de nable by an EFS in HEFS(1; 0; 1) resp. HEFS( 0; 1) HEFS( 1; 1; 1) HEFS( 2; 2; 1) Finally, we formulate the termination for HEFSs, which are motivated by the acyclicity of EFSs [6, 10, 13]. De nition 7 Let S be a signature and H be an EFS over S. The dependency graph of H is a possibly in nite directed graph GH = Atom S ; E) such that there exists an edge from A to B, i.e. A; B) 2 E, i there exist a ground instance C of some clause in H such that A = hd(C) and B 2 bd(C) ....

K. Apt, M. Bezem, Acyclic programs, in: Proc. 7th Internat. Conf. on Logic Programming (The MIT Press, 1990) 617-633.

....that irrelevant de nitions are also processed. This can be very costly. Fortunately, this general consistency checking is unnecessary in many cases. Indeed, for a broad class of de nitions, consistency is known to hold . For example, this is the case with hierarchical and acyclic rule sets [1]. Also the de nitions used in the temporal theories considered in the following sections, have the consistency property. The following de nition formalises the consistency property. De nition 3.2 Given is a theory D consisting of de nitions, J a class of interpretations of the function ....

....nitions, J a class of interpretations of the function symbols and the open predicates. A theory T = D [ T is i de nitional w.r.t. J i for each J 2 J , there exists a unique model M of D that coincides with J on the function and open symbols. Theorem 3. 1 Let D be an acyclic set of de nitions [1], J the class of Herbrand interpretations of the function symbols and the open predicates. D is i de nitional w.r.t. J . This theorem is proven in [1] Theorem 3.2 Let T = D [ T be a theory, D a set of de nitions which is i de nitional w.r.t. to a class J of interpretations of open ....

[Article contains additional citation context not shown here]

K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the International Conference on Logic Programming, pages 579-597. MIT Press, 1990.

....from research in the domain of temporal reasoning. Temporal reasoning is an excellent domain for testing nonmonotonic reasoning techniques because of the frame problem. The frame axiom has a correct representation in situation and event calculus with negation as failure, as was illustrated in [1] for the famous Yale Turkey Shooting problem. A major restriction of negation as failure is its incapacity of representing incomplete knowledge. The original event calculus only supports the prediction of a goal state, starting from a complete description of the initial state and the set of ....

K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the seventh International Conference on Logic Programming, pages 579-597. MIT press, 1990.

....and t is a numeric constant representing a time point. The proof of this proposition is in the appendix. This proof is inductive and shows the completeness of the program relative to the ground literals of the program. An alternative is to appeal to a more general result due to Apt and Bezem [7]. It can be proven that the logic program presented in this section falls in the category of acyclic logic programs defined by Apt and Bezem [7] Acyclic logic programs are defined in the following manner: Let P be a program and M be a mapping from the elements of the Herbrand Base of the program ....

....the completeness of the program relative to the ground literals of the program. An alternative is to appeal to a more general result due to Apt and Bezem [7] It can be proven that the logic program presented in this section falls in the category of acyclic logic programs defined by Apt and Bezem [7]. Acyclic logic programs are defined in the following manner: Let P be a program and M be a mapping from the elements of the Herbrand Base of the program to the natural numbers. A mapping M for program P is acyclic if for any ground instance of a clause in P of the form: A: L 1 ; L n : M ....

Apt, K., and Bezem, M. Acyclic programs. In Logic Programming: Proceedings of the Seventh International Conference. (1990), D. Warren and P. Szeredi, Eds., pp. 617--633.

....also after the event E. This statement is often called the inertia axiom. The following locally strati ed program, called YSP, formalizes the above statements, and in particular, clauses 1 5 correspond to statements (s1) s5) respectively. Our YSP program is similar to the one of Apt and Bezem [1]. 1. holds(alive ; Program YSP 2. holds(loaded ; load jS] 3. holds(dead ; shoot jS] holds(loaded ; S) 4. ab(alive ; shoot ; S) holds(loaded ; S) 5. holds(F; EjS] fact(F ) event(E) holds(F; S) ab(F; E; S) 6. event(load ) 7. event(shoot) 8. event(wait) 9. fact(alive) ....

K. R. Apt and M. Bezem. Acyclic programs. In D.H.D. Warren and P. Szeredi, editors, Proceedings of the 7th International Conference on Logic Programming, Jerusalem, Israel, pages 617633. MIT Press, 1990.

....to represent the frame axiom correctly. A nonmonotonic reasoning technique that was mistakenly not considered by these authors is negation as failure. It has been shown that the YTS representation in situation calculus or event calculus with negation as failure solves the problem correctly ([1], 4] 5] Negation as failure alone is not sufficient for representing many temporal reasoning problems. A major restriction is its incapacity of representing incomplete knowledge. The original event calculus only supports the prediction of a goal state, starting from a complete description of ....

K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the International Conference on Logic Programming, pages 579--597. MIT press, 1990.

....is well de ning in every context are well known from the logic programming literature: non recursive de nitions positive recursive de nitions strati ed de nitions Other properties guarantee well de ning de nitions in some speci c context. Inductive de nitions corresponding to acyclic [3] or locally strati ed logic programs [21] are well de ning in the context of Herbrand interpretations. It follows from theorem 1 that a well founded de nition in context I is also well de ning in I. A syntactical criterion that guarantees well foundedness and hence wellde ning ness is the ....

K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the International Conference on Logic Programming, pages 579-597. MIT press, 1990.

....) The clause Noninertial(loaded; load; S) may be dropped from this program without effect on the semantics of Holds 2. In general, all Noninertial=3 rules for initiating effects of actions may be dropped, without effect on the semantics of Holds 2. DY TS strongly resembles the YTS solution in [1] and in [14] For example, 1] proposes a Prolog program analogous to D Y TS : Holds(alive; s 0 ) Holds(F; Result(A; S) Holds(F; S) Noninertial(F; A; S) Holds(loaded; Result(load; S) Noninertial(loaded; shoot; S) Noninertial(alive; shoot; S) Holds(loaded; S) Note that this ....

....load; S) may be dropped from this program without effect on the semantics of Holds 2. In general, all Noninertial=3 rules for initiating effects of actions may be dropped, without effect on the semantics of Holds 2. DY TS strongly resembles the YTS solution in [1] and in [14] For example, [1] proposes a Prolog program analogous to D Y TS : Holds(alive; s 0 ) Holds(F; Result(A; S) Holds(F; S) Noninertial(F; A; S) Holds(loaded; Result(load; S) Noninertial(loaded; shoot; S) Noninertial(alive; shoot; S) Holds(loaded; S) Note that this program entails the two FOL ....

[Article contains additional citation context not shown here]

K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the International Conference on Logic Programming, pages 579--597. MIT press, 1990. 26

....clause Noninertial(Loaded; Load; s) true may be dropped from this program without effect on the semantics of Holds 2. In general, all Noninertial=3 rules for initiating effects of actions may be dropped, without effect on the semantics of Holds 2. D 0 strongly resembles the YTS solution in [1]. They propose a Prolog program analogous to the one obtained from D 0 by substituting the program clause: Holds(Alive; S 0 ) true for the program clauses Holds(f; S 0 ) Initially(f) and Noninertial(Loaded; Load; s) true and the two integrity constraints of D 0 . Note that the resulting ....

....one obtained from D 0 by substituting the program clause: Holds(Alive; S 0 ) true for the program clauses Holds(f; S 0 ) Initially(f) and Noninertial(Loaded; Load; s) true and the two integrity constraints of D 0 . Note that the resulting program entails the two integrity constraints. [1] proves that the resulting program is acyclic. The same holds for D 0 , and in fact for all transformed domain descriptions: Proposition 3.1 The translation D of any domain description D is acyclic. Several types of semantics have been defined for incomplete programs [3] 14] 19] 7] Due to ....

[Article contains additional citation context not shown here]

K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the International Conference on Logic Programming, pages 579--597. MIT press, 1990.

....paragraph: M 0 = OE; M 1 = fpg. This is a finite fair NMGE, but the set of abductive atoms in the model ( OE) is not an abductive solution. There is an important class of definite abductive programs where the duality is perfect, namely for definite abductive acyclic programs and bounded queries [1]. For these programs and queries, an SLD Abduction tree is always finite. Using this fact and the completeness Theorem 4.2, it is easy to prove that the abductive atoms in each model of the dual theory form an abductive solution. 6 Implementing NMGE We have implemented two instances of the NMGE ....

K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the International Conference on Logic Programming, pages 579--597. MIT press, 1990.

....certain conditions negative literals in the body of rules (as for the :init literals in the effect rules considered before) some of them including the possibility of positive loops as in the gear wheels example. In particular, ffl predicate completion [8] is adequate for acyclic rule sets [2]; ffl circumscription [26] is adequate for positive rule sets; ffl prioritized circumscription [20] is adequate for stratified rule sets; ffl perfect model semantics is adequate for stratified rule sets [32] ffl Iterated Inductive Definition semantics is adequate for stratified rule sets ....

....of a rule before propagating the effect described by the rule. If this assumption is not satisfied, the completion semantics cannot be used, and in general we cannot expect any semantics to reason correctly on delays that have not been modelled (we will return to this issue in section 6) In [2], it is shown that the completion of a hierarchical logic program has one unique model. It follows that given any state S and set of actions A, a hierarchical effect theory Pi e has exactly one model. This is the model M S;A; Pie used to define the update set and the transition function, using ....

[Article contains additional citation context not shown here]

K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the International Conference on Logic Programming, pages 579--597. MIT press, 1990.

....However, this is not the ambiguity problem that I am referring at. There is a deeper problem. There is a substantial overlap between the different LP logics. For example, for acyclic normal programs, completion semantics, the stable semantics and the well founded semantics are known to coincide [1]. For stratified programs, stable, well founded and perfect semantics coincide. In general, we should expect that: a) the declarative reading underlying the different semantics are equivalent for programs for which different semantics coincide; b) each logic consisting of a pair of syntax and ....

K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the International Conference on Logic Programming, pages 579--597. MIT Press, 1990.

....in every context are well known from the logic programming literature: ffl non recursive definitions ffl positive recursive definitions ffl stratified definitions Other properties guarantee well defining definitions in some specific context. Inductive definitions corresponding to acyclic (Apt Bezem 1990) or locally stratified logic programs (Przymusinski 1988) are welldefining in the context of Herbrand interpretations. It follows from theorem 1 that a well founded definition in context I is also well defining in I. A syntactical criterion that guarantees wellfoundedness and hence ....

Apt, K., and Bezem, M. 1990. Acyclic programs. In Proc. of the International Conference on Logic Programming, 579--597. MIT press.

....problem as a whole, at clarifying the importance of certain subproblems, and at providing conceptually clear frameworks for studying the di erent trade o s in termination analysis in general. A second line of work has lled this gap. Especially the work of Apt, Bezem and Pedreschi (see e.g. [Apt and Bezem 1991; Apt and Pedreschi 1990; 1991; Bezem 1992] but also work of others, such as Bossi et al. Bossi et al. 1991; 1992] studied the problem from a more mathematical perspective, providing more insight into the various components of a Department of Computer Science, K.U.Leuven, Celestijnenlaan ....

Apt, K. and Bezem, M. 1991. Acyclic programs. New Generation Computing 9, 335-363.

....Contraction Theorem [48] A contraction mapping f on a complete metric space has a unique fixed point. The sequence x; f(x) f(f(x) converges to this fixed point for any x. 3. Acyclic Logic Programs Acyclic logic programs were investigated by Cavedon [9] 2 as well as Apt and Bezem [3, 4]. They are a subclass of the class of locally stratified programs defined by Przymusinsky [37] and enjoy several desirable properties like the fact that for each acyclic program P the meaning function TP has a unique fixed point MP , that MP is a minimal model and the perfect model 3 of P , and ....

....discussed further in Section 7. It is straightforward to generate an injective level mapping for a given program because the set of ground atoms over an alphabet with a finite number of function and predicate symbols can be enumerated. The property of being an acyclic program is undecidable (see [3]) and we conjecture that it is also undecidable whether a given program is acyclic with respect to an injective level mapping. We use the level mapping k k to define a mapping R from the set 2 BP of interpretations for a logic program P to real numbers: Definition 2. The mapping R : 2 BP ....

K.R. Apt and M. Bezem. Acyclic Programs. In D.H.D. Warren and P. Szeredi, editors, Logic Programming, Proceedings of the Seventh International Conference, Jerusalem, Israel, June 18-20, MIT Press pp. 617--633, 1990.

....the atom A. A program (rule, atom, term) is ground if it contains no variable. An NLP P is acyclic if there is a level mapping from the ground atoms of P to the natural numbers, such that for any ground rule (1) from P , the level of A 0 is higher than the level of every A i (i = 1; n) (Apt and Bezem, 1991) . P is Horn if no rule in P contains negation as failure, that is, m = n holds for every rule of the form (1) in P . P is definite if it is a Horn program without integrity constraints. The semantics of NLPs is given by the stable model semantics (Gelfond and Lifschitz, 1988) Given any NLP P ....

K. R. Apt and M. Bezem (1991). Acyclic programs. New Generation Computing, 9:335--363.

....theory when there is more than one agent) The idea is, rather than using disjunction to handle uncertainty, to allow agents, including nature, to make choices from a choice space, and use a restricted underlying logic to specify the consequences of the choices. We can adopt acyclic logic programs (Apt Bezem 1991) under the stable model semantics (Gelfond Lifschitz 1988) as the underlying logical formalism. This logic includes no uncertainty in the sense that every acyclic logic program has a unique stable model. 3 All uncertainty is handled by independent stochastic mechanisms. A deterministic logic ....

....and only if either h 2 gr(F) or there is a rule h b in gr(F) such that b is true in M. Conjunction f g is true in M if both f and g are true in M. Disjunction f g is true in M if either f or g (or both) are true in M. Negation f is true in M if and only if f is not true in M. Definition 2. 2 (Apt Bezem 1991) A logic program F is acyclic if there is an assignment of a natural number to each element of the Herbrand base of F such that, for every rule in gr(F ) the number assigned to the atom in the head of the rule is greater than the number assigned to each atom that appears in the body. Acyclic ....

[Article contains additional citation context not shown here]

Apt, K. R. & Bezem, M. (1991). Acyclic programs, New Generation Computing 9(3-4): 335--363.

....there is an extension of the default theory in which the action of waiting unloads the gun. Morris [1988] showed that formalizing the frame default with the non normal default : Ab(f; a; s) Holds(f; s) j Holds(f; Result(a; s) 2.8) solves the Yale Shooting Problem. Evans [1989] and Apt and Bezem [1990] represent properties of actions in logic programming languages with negation as failure. Gelfond and Lifschitz [1993] point out the 1 A default of the form ff : w=w is called a normal default. 14 advantages of representing actions in extended logic programs (logic programs that can represent ....

Krzysztof Apt and Marc Bezem. Acyclic programs. In David Warren and Peter Szeredi, editors, Logic Programming: Proc. of the Seventh Int'l Conf., pages 617--633, 1990.

No context found.

Apt, K.R. and M. Bezem (1990). Acyclic Programs. In: 7th International Conference on Logic Programming. MIT Press. Jerusalem, Israel.

No context found.

K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the International Conference on Logic Programming, pages 579--597. MIT Press, 1990.

No context found.

K.R. Apt and M. Bezem. Acyclic programs. In D.H.D. Warren and P. Szeredi, editors, Proceedings Seventh International Conference on Logic Programming, pages 617--633. The MIT Press, 1990.

No context found.

Apt, K., and M. Bezem. Acyclic programs. In D. Warren and P.Szeredi (Eds.), Logic programming: Proc. 7th Int'l Conf., 1990, pp. 617-633.

No context found.

Apt, K., and M. Bezem. Acyclic programs. In D. Warren and P.Szeredi (Eds.), Logic programming: Proc. 7th Int'l Conf., 1990, pp. 617--633.

No context found.

Apt, K. R. and Bezem, M. 1991. Acyclic programs. New Generation Computing 9, 335-363.

No context found.

) K.R. Apt and M. Bezem. Acyclic programs. In Proceedings of the 7th Interna-

First 50 documents  Next 50

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