Alessandro Armando, Claudio Castellini, and Enrico Giunchiglia. SAT-based procedures for temporal reasoning. In Proceedings of the 5th European Conference on Planning, pages 97--108, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in [SS90] Several researchers investigated the extension of SAT based bounded model checking from finite state systems to systems with unbounded variables representing clocks. A solver for a logic similar to di#erence logic was used for artificial intelligence temporal planning problems in [ACG99] In [ACKS02, ABC 02] the authors develop an extended SAT solver to verify timed automata against temporal logic specifications. Although this work has the same motivation as this thesis, the approach it adopts is quite di#erent: the interaction between the Boolean and the numerical part is ....

A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Proceedings of ECP'99, LNCS. Springer, 1999.

....of the solver, while some preliminary experimental results are described in Section 6. We conclude with some related work. 2 Difference Logic In this section we define the class of formulae that we consider. This class has already been used elsewhere (see e.g. MLAH99,LPWY99,ABK 97,BM00,ACG99] and is probably part of folklore, but to give it a name let us call it difference logic (DL) We use two slightly different variants, DLZ and DLR depending on the domain of the numerical variables. Definition 1 (Difference Logic) Let B 1 , B 2 , be a set of Boolean variables ....

....experiments required less than 10MB. 7 Related Work and Conclusions The idea to extend the applicability of SAT based verification from finite state systems to systems augmented with unbounded variables or clocks is a very natural one and has been pursued independently by several groups. In [ACG99] a solver for a similar logic was applied to AI temporal planning problems. The closest work to ours is that of [ABC 02,ACKS02] where the authors develop an extended SAT solver to verify timed automata against temporal logic specifications. The major differences with respect to the present ....

A. Armando, C. Castellini and E. Giunchiglia, SAT-based Procedures for Temporal Reasoning, Proc. ECP'99, LNCS, Springer, 1999.

....in the performance of SAT solvers. Such successes have pushed several researchers interested in satisfiability modulo theories to find ways to harness the power of modern DPLL based solvers by coupling them with decision procedures. Possibly the first work along these lines is that described in [1]. Very recent, independent research on the same idea is reported in [2, 4, 8] Very briefly, the idea common to all these works is the following: given a set of ground clauses to be checked for satisfiability in some theory , use an o# the shelf solver to obtain a propositional model of the ....

....these works is the degree of laziness with which the decision procedure is invoked. Some invoke the procedure after a complete propositional model has been found, others invoke it incrementally, as the model is being built, in order to minimize backtracking on wrong choices. The approaches in [1, 2, 4, 8] are all described procedurally. In this paper, we propose instead a general declarative framework, given as a sequent calculus, for extending the DPLL method with decision procedures. While the calculus is general enough that it can model (with minor changes) each of the approaches above, it also ....

Alessandro Armando, Claudio Castellini, and Enrico Giunchiglia. SAT-based procedures for temporal reasoning. In S. Biundo and M. Fox, editors, Proceedings of the 5th European Conference on Planning (Durham, UK), volume 1809 of Lecture Notes in Computer Science, pages 97--108. Springer, 2000.

....of the ites in terms of the usual boolean connectives can blow up in size. An alternative stream of research to handle combination of domain speci c and propositional reasoning consists of integrating satis ability procedures with generic propositional satis ability (SAT) solvers [BDS02, dMR02, ACG00, ABC 02] see [Tin02] for a rational reconstruction of the combination of the Davis Putnam procedure and satis ability procedures for rst order theories) In this approach, atoms are abstracted to propositional constants, the resulting propositional formulae are sent to the SAT solver which ....

A. Armando, C. Castellini, and E. Giunchiglia. SAT-Based Procedures for Temporal Reasoning. In 5th European Conference on Planning, ECP'99, Durham, UK, 1999, number 1809 in LNCS, pages 97108. Springer-Verlag, 2000.

.... and effident temporal reasoning is essential to a number of areas in Artifidal Intelligence (AI) Over the past few years, a new constraint based formalism for temporal reasoning has been developed to represent and reason about Disjunctive Temporal Problems (DTPs) Stergiou and Koubarakis 1998; Armando, Castellini et al. 1999; Oddi and Cesta 2000] The class of DTPs is significantly more expressive than other problems already studied in constraint based temporal reasoning. It extends the well known Simple Temporal Problem (STP) Dechter, Meiri et al. 1991] by allowing disjunctions and the Temporal Constraint ....

....to make inferences regarding the infeasibility of certain regions of the search. In this section we describe three methods previously considered in the literature: ontZt Directed Balcjumping (CDB) used in [Stergiou and Koubarakis 2000] emant B anch ng, SB) used in [Oddi and Cesta 2000] and [Armando, Castellini et al. 1999]) and Removal o ubsumed lZatiables (RSV) used in [Armando, Castellini et al. 1999] In the next section we will add No flood Re ovchg (NR) also called no good learning) and hence throughout both these sections we will be particularly concerned with the theoretical and technical issues that ....

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Armando, A., C. Castellini and E. Giunchiglia (1999). SAT-based Procedures for Temporal Reasoning. 5th European Conference on Planning (ECP-99).

.... of a DTP is NP hard, and because DTPs include non binary constraints, it is difficult to use path consistency on them to increase efficiency[3] However, several recent papers have presented heuristic techniques that significantly decrease the typical time needed to check DTP consistency [1, 21, 12, 22]. Recently, STPs have also been extended to take into account tem poral uncertainty. In STPs (as in TCSPs and DTPs) the constraint between any two time points x and y specifies an interval that is con trollable: i.e. the execution agent can choose for (y x) any of the values within the ....

....(go x y) denotes the action of going from location x to location y. A node labeled 2 If the action has temporal duration, the model includes two nodes for every action: one that denotes the time at which execution of the action begins, and another that denotes the time at which it ends. 7 I [1,1] (obs (roadb s) Figure . The skiing plan as a Conditional Simple Temporal Problem. All non annotated edges are assumed [0, oc] and all non annotated nodes are assumed labeled True. go x y) i.e. with subscript S, indicates the event of starting the action (go x y) similarly (go x y)E ....

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Armando, A., C. Castellini, and E. Giunchiglia: 1999, 'Sat-Based Procedures for Temporal Reasoning'. In: 5th European Conference on Planning (ECP-99).

.... the consistency of a DTP is NP hard, and because DTPs include non binary constraints, it is dicult to use path consistency on them to increase eciency[3] However, several recent papers have presented heuristic techniques that signi cantly decrease the typical time needed to check DTP consistency [1, 21, 12, 22]. Recently, STPs have also been extended to take into account temporal uncertainty. In STPs (as in TCSPs and DTPs) the constraint between any two time points x and y speci es an interval that is controllable: i.e. the execution agent can choose for (y x) any of the values within the allowed ....

....temporal duration, the model includes two nodes for every action: one that denotes the time at which execution of the action begins, and another that denotes the time at which it ends. 7 Figure 2. The skiing plan as a Conditional Simple Temporal Problem. All non annotated edges are assumed [0, 1] and all non annotated nodes are assumed labeled T rue. go x y) S , i.e. with subscript S, indicates the event of starting the action (go x y) similarly (go x y) E denotes the event of ending such an action (and arriving at y) The observation events; obs (road x y) denotes observing the ....

Armando, A., C. Castellini, and E. Giunchiglia: 1999, `Sat-Based Procedures for Temporal Reasoning'. In: 5th European Conference on Planning (ECP-99).

....and has thus bene ted of the nancial contribution of the Commission through the IHP programme. We implemented the approach in the Math SATsolver, based on the SIM package for propositional satis ability. An experimental evaluation was carried out on tests arising from temporal reasoning [2] and formal veri cation of timed systems [3] In the rst class of problems, we compare our results with the results of the specialized system; although Math SAT is able to tackle a wider class of problems, it runs faster that the Tsat solver, that is specialized to a problem class. In the second ....

....point. 3. 4 Improvements optimizations We describe some improvements and optimizations for Math SAT, some of which come from adapting to our domain improvements and optimizations of the DPLLbased procedures for modal logics [12, 14, 13] and for temporal reasoning and resource planning [2, 19]. Preprocessing atoms One potential source of ineciency for the procedure of Figure 1 is the fact that semantically equivalent but syntactically di erent atoms are not recognized to be identical [resp. one the negation of the other] and thus they may be assigned di erent [resp. identical] truth ....

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A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Proc. European Conference on Planning, ECP-99, 1999.

....not expressive enough for representing many real world problems. For example, problem domains like temporal reasoning, resource planning, veri cation of systems with numerical data values or of timed systems, often require handling also constraints on integer or real valued quantities (see, e.g. [1, 18, 17, 19]) Moreover, some problem domains like model checking often require an explicit representation of integers and arithmetic operators, which simple boolean expressions are not good at representing eciently (see, e.g. 17, 14] On the other hand, mathematical reasoners, like computer algebra ....

....and to use a (modi ed) Davis Putnam Longemann Loveland (DPLL) SAT solver [6] for the former and a pure domain speci c procedure for the latter. So far the SAT based approach proved very e ective in various problem domains like, e.g. modal and description logics [12, 8] temporal reasoning [1], resource planning [18] In this paper we present the foundations and the basic algorithms for a new class of procedures for solving boolean combinations of mathematical propositions, which combine SAT solvers and mathematical reasoners. The ultimate goal is to develop solvers able to handle ....

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A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Proc. European Conference on Planning, CP-99, 1999.

....of selected disjuncts that may need to be considered; the challenge is to nd ways to eciently explore the space of disjunct combinations. This has been done by casting the disjunct selection problem as a constraint satisfaction processing (CSP) problem [18, 13] or a satis ability (SAT) problem [1]. Epilitis combines and extends the previous approaches, in particular by adding no good learning, and achieves a speed up of two orders of magnitude on a range of benchmark problems [19] For typical problems we have so far studied in the Autominder domain, performance is well within the ....

E. Giunchiglia A. Armando, C. Castellini. Sat-based procedures for temporal reasoning. In 5th European Conference on Planning, 1999.

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A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Lecture Notes in Computer Science, volume 1809, pages 97-108, 1999.

No context found.

Alessandro Armando, Claudio Castellini, and Enrico Giunchiglia. SAT-based procedures for temporal reasoning. In Susanne Biundo and Maria Fox, editors, Proceedings of the 5th European Conference on Planning (Durham, UK), volume 1809 of Lecture Notes in Computer Science, pages 97--108. Springer, 2000.

.... Giunchiglia et al. 1998, Giunchiglia et al. 2000b ] SAT based decision procedures for decidable fragments of rst order logic are presented in [ Armando and Giunchiglia, 1989, Armando and Giunchiglia, 1993 ] Finally, SAT based decision procedures have been proposed in temporal reasoning [ Armando et al. 1999 ] and planning [ Giunchiglia et al. 2000b, Giunchiglia et al. 2001, Wolfman and Weld, 1999 ] In this paper, we present a unifying perspective on the various SAT based approaches to the di erent reasoning tasks previously considered. In particular, in Section 2 we present the common ideas of ....

....by the proposed optimization is to rule out such assignments. For instance, by adding the constraint :x = y y = x (2) to (1) we obtain a formula which is readily found unsatis able by DLL Solve. In the context of SAT based procedures, the idea of adding constraints has been introduced in [ Armando et al. 1999 ] In that paper, all pairs of mutually inconsistent inequalities (i.e. x y 0 and x y 5) are detected a priori at a reasonable cost, and for each such pair a constraint is added. As a result, the search is greatly reduced. The idea can be generalized to n uples of inconsistent inequalities, ....

[Article contains additional citation context not shown here]

A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Lecture Notes in Computer Science, volume 1809, pages 97-108, 1999.

....one domain consistent assignment is found i.e. the input formula is consistent or no more assignments are available i.e. the input formula is inconsistent. So far the SAT based approach proved very e ective in various problem domains like, e.g. modal logics [GS96a] temporal reasoning [ACG99], resource planning [WW99] In particular, the latter two proved rather e cient in combining SAT reasoning with Linear Programming (LP) Now we want to focus our research on combining SAT non only with LP systems, but also with math constraint solvers and or computer algebra systems. The ....

A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Proc. ECP-99, 1999.

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Alessandro Armando, Claudio Castellini, and Enrico Giunchiglia. SAT-based procedures for temporal reasoning. In Proceedings of the 5th European Conference on Planning, pages 97--108, 1999.

No context found.

A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Proc. European Conference on Planning, CP-99, 1999.

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Alessandro Armando, Claudio Castellini, and Enrico Giunchiglia. SAT-based procedures for temporal reasoning. In ECP, pages 97--108, 1999.

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A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Proc. European Conference on Planning, CP-99, 1999.

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A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Proc. European Conference on Planning, CP-99, 1999.

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A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Procs. of the 5th European Conference on Planning, LNCS 1809, pages 97--108. Springer, 2000.

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A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Proceedings of the Fifth European Conference on Planning (ECP-99), 1999.

No context found.

A. Armando, C. Castellini, and E. Giunchiglia. SAT-based procedures for temporal reasoning. In Procs. of the 5th European Conference on Planning, LNCS 1809, pages 97--108. Springer, 2000.

No context found.

Alessandro Armando, Claudio Castellini, and Enrico Giunchiglia. SAT-Based Procedures for Temporal Reasoning. In S. Biundo and M. Fox, editors, Proceedings of the 5th European Conference on Planning (Durham, UK), volume 1809 of Lecture Notes in Computer Science, pages 97-108. Springer, 2000.

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