The availability of decision procedures for combinations of boolean and linear mathematical propositions opens the ability to solve problems arising from real-world domains such as verification of timed systems and planning with resources. In this paper we present a general and efficient approach to the problem, based on two main ingredients. The first is a DPLL-based SAT procedure, for dealing efficiently with the propositional component of the problem. The second is a tight integration, within the DPLL architecture, of a set of mathematical deciders for theories of increasing expressive power. A preliminary experimental evaluation shows the potential of the approach.

This paper describes Autominder, a cognitive orthotic system intended to help older adults adapt to cognitive decline and continue the satisfactory performance of routine activities, thereby potentially enabling them to remain in their own homes longer. Autominder achieves this goal by providing adaptive, personalized reminders of (basic, instrumental, and extended) activities of daily living. Cognitive orthotic systems on the market today mainly provide alarms for prescribed activities at fixed times that are specified in advance. In contrast, Autominder uses a range of AI techniques to model an individual's daily plans, observe and reason about the execution of those plans, and make decisions about whether and when it is most appropriate to issue reminders. Autominder is currently deployed on a mobile robot, and is being developed as part of the Initiative on Personal Robotic Assistants for the Elderly (the Nursebot project)

In this paper we study the consistency problem for a set of disjunctive temporal constraints [Stergiou and Koubarakis, 1998]. We propose two SAT-based procedures, and show that|on sets of binary randomly generated disjunctive constraints|they perform up to 2 orders of magnitude less consistency checks than the best procedure presented in [Stergiou and Koubarakis, 1998]. On these tests, our experimental analysis conrms Stergiou and Koubarakis's result about the existence of an easy-hard-easy pattern whose peak corresponds to a value in between 6 and 7 of the ratio of clauses to variables.

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). The class of DTPs is significantly more expressive than other problems previously studied in constraint-based temporal reasoning. In this paper we present a new algorithm for DTP solving, called Epilitis, which integrates strategies for efficient DTP solving from the previous literature, including conflict-directed backjumping, removal of subsumed variables, and semantic branching, and further adds no-good recording as a central technique. We discuss the theoretical and technical issues that arise in successfully integrating this range of strategies with one another and with no-good recording in the context of DTP solving. Using an implementation of Epilitis, we explore the effectiveness of various combinations of strategies for solving DTPs, and based on this analysis we demonstrate that Epilitis can achieve a nearly two order-of-magnitude speed-up over the previously published algorithms on benchmark problems in the DTP literature.

Temporal constraints pose a challenge for conditional planning, because it is necessary for a conditional planner to determine whether a candidate plan will satisfy the specified temporal constraints. This can be diflCicult, because temporal assignments that satisfy the constraints associated with one conditional branch may fail to satisfy the constraints along a different branch. In this paper we adch'ess this challenge by developing the Conditional Temporal Problem (CTP) formalism, an extension of standard temporal constraint-satisfaction processing models used in non-conditional temporal planning. Specifically, we augment temporal CSP frameworks by (1) adding observation nodes, and (2) attaching labels to all nodes to indicate the situation(s) in which each will be executed. Our extended framework allows for the construction of conditional plans that are guaranteed to satisfy complex temporal constraints. Importantly, this can be achieved even while allowing for decisions about the precise timing of actions to be postponed until execution time, thereby adding flexibility and making it possible to dynamically adapt the plan in response to the observations made during execution. We also show that, even for plans without explicit quantitative temporal constraints, our approach fixes a problem in the earlier approaches to conditional planning, which resulted in their being incomplete.

... an opportunity for the design of intelligent technology. This paper focuses on one type of assistive technology, cognitive orthotics, which can help people adapt to cognitive declines and continue satisfactory performance of routine activities, thereby potentially enabling them to remain in their own homes longer. Existing cognitive orthotics mainly provide alarms for prescribed activities at fixed times that are specified in advance. In contrast, we describe Autominder, a system we have designed that uses AI planning and plan management technology to carefully model an individual's daily plans, attend to and reason about the execution of those plans, and make flexible and adaptive decisions about when it is most appropriate to issue reminders. The paper concentrates on one of Autominder's three main components, the Plan Manager; other papers in this volume describe its other components (Colbry, Peintner, & Pollack 2002; McCarthy & Pollack 2002).

Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra contains exactly eighteen maximal tractable subalgebras, and reasoning in any fragment not entirely contained in one of these subalgebras is NP-complete. We obtain this result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using an algebraic technique for identifying maximal subalgebras with a given property.

Abstract. Recent improvements in propositional satisfiability techniques (SAT) made it possible to tackle successfully some hard real-world problems (e.g. model-checking, circuit testing, propositional planning) by encoding into SAT. However, a purely boolean representation is not expressive enough for many other real-world applications, including the verification of timed and hybrid systems, of proof obligations in software, and of circuit design at RTL level. These problems can be naturally modeled as satisfiability in Linear Arithmetic Logic (LAL), i.e., the boolean combination of propositional variables and linear constraints over numerical variables. In this paper we present MATHSAT, a new, SAT-based decision procedure for LAL, based on the (known approach) of integrating a state-of-the-art SAT solver with a dedicated mathematical solver for LAL. We improve MATHSAT in two different directions. First, the top level procedure is enhanced, and now features a tighter integration between the boolean search and the mathematical solver. In particular, we allow for theory-driven backjumping and learning, and theory-driven deduction; we use static learning in order to reduce the number of boolean models that are mathematically inconsistent; we exploit problem clustering in order to partition

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The computerization of clinical practice guidelines is a significant scientific challenge for the medical informatics community. One frequently reported factor hindering this objective is the existence of deficiencies within guideline knowledge. In this paper, we focus on the detection of flaws within temporal scheduling constraints. Temporal scheduling constraints are important elements of therapy management, and are frequently incorporated in clinical practice guidelines. We present a suitable verification method that is based on calculating the minimal network of temporal constraints on the execution of guideline activities. Our method serves three purposes: (1) it checks whether temporal scheduling constraints are consistent with scheduling constraints implied by control flow operators and the hierarchical structuring of a guideline; (2) it yields suggestions for an equivalent, yet more explicit representation of non-minimal constraints; (3) it can be used by the guideline interpreter to assemble feasible time intervals for the execution of each guideline activity. We evaluate our approach by applying it to a guideline specified in the Asbru language. For this purpose, we implemented a prototype verifier. Although we concentrate on the guideline representation language Asbru as the demonstration medium of our method within this paper, our approach can be reused to verify several alternative guideline-representation formats.