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To appear in the proceedings of LPAR 21. Solving complex problems can involve non-trivial combinations of distinct knowledge bases and problem solvers. The Algebra of Modular Systems is a knowledge representation framework that provides a method for formally specifying such systems in purely semantic terms. Formally, an expression of the algebra defines a class of structures. Many expressive formalism used in practice solve the model expansion task, where a structure is given on the input and an expansion of this structure in the defined class of structures is searched (this practice overcomes the common undecidability problem for expressive logics). In this paper, we construct a solver for the model expansion task for a complex modular systems from an expression in the algebra and black-box propagators or solvers for the primitive modules. To this end, we define a general notion of propagators equipped with an explanation mechanism, an extension of the alge- bra to propagators, and a lazy conflict-driven learning algorithm. The result is a framework for seamlessly combining solving technology from different domains to produce a solver for a combined system.
Janhunen, Tomi (Helsinki Institute for Information Technology and Aalto University) | Tasharrofi, Shahab (Helsinki Institute for Information Technology and Aalto University) | Ternovska, Eugenia (Simon Fraser University)
Special-purpose propagators speed up solving logic programs by inferring facts that are hard to deduce otherwise. However, implementing special-purpose propagators is a non-trivial task and requires expert knowledge of solvers. This paper proposes a novel approach in logic programming that allows (1) logical specification of both the problem itself and its propagators and (2) automatic incorporation of such propagators into the solving process. We call our proposed language P [ R ] and our solver SAT-to-SAT because it facilitates communication between several SAT solvers. Using our proposal, non-specialists can specify new reasoning methods (propagators) in a declarative fashion and obtain a solver that benefits from both state-of-the-art techniques implemented in SAT solvers as well as problem-specific reasoning methods that depend on the problem's structure. We implement our proposal and show that it outperforms the existing approach that only allows modeling a problem but does not allow modeling the reasoning methods for that problem.
We propose a versatile framework for combining knowledge bases in modular systems with preferences. In our formalism, each module (knowledge base) can be specified in a different language. We define the notion of a preference-based modular system that includes a formalization of meta-preferences. We prove that our formalism is robust in the sense that the operations for combining modules preserve the notion of a preference-based modular system. Finally, we formally demonstrate correspondences between our framework and the related preference formalisms of cp-nets and preference-based planning. Our framework allows one to use these preference formalisms (and others) in combination, in the same modular system.
We address the problem of providing a logical formalization of arithmetic in declarative modelling languages for NP search problems. The challenge is to simultaneously allow quantification over an infinite domain such as the natural numbers, provide natural modelling facilities, and control expressive power of the language. To address the problem, we introduce an extension of the model expansion (MX) based framework to finite structures embedded in an infinite secondary structure, together with "double-guarded" logics for representing MX specifications for these structures. The logics also contain multi-set functions (aggregate operations). Our main result is that these logics capture the complexity class NP on "small-cost" arithmetical structures.