Satisfiability for Propositional Contexts

We propose a sound and complete satisfiability algorithm for propositional multi-context systems. In essence, the algorithm is a distribution policy built on top of local reasoning procedures, one for each context, which can be implemented by (a diversity of) customized state-of-the-art SAT solvers. The foremost intuition that has motivated our algorithm, and the very potential strength of contextual reasoning, is that of keeping reasoning as local as possible. In doing so, we improve on earlier established complexity results by Massacci. Moreover, our approach could be applied to enhance recent proposals by Amir and Mcilraith towards a new partitionbased reasoning paradigm; particularly, our formalism allows for a more expressive description of interpartition relations, and we provide an algorithm that is explicitly designed to deal with this expressiveness. Introduction The establishment of a solid paradigm for contextual knowledge representation and contextual reasoning is of paramount importance for the development of sophisticated theory and applications in AI. McCarthy (1987) pleaded for a formalization of context as a possible solution to the problem of generality, whereas Giunchiglia (1993a) emphasized the principle of locality – reasoning based on large (common sense) knowledge bases can only be effectively pursued if confined to a manageable subset (context) of that knowledge base. Contextual knowledge representation has been formalized in several ways. Most notable are the propositional logic of context developed by McCarthy, Buvač and Mason (1993; 1998), and the multi-context systems devised by Giunchiglia and Serafini (1994), which later became associated with the local model semantics (Ghidini & Giunchiglia 2001). Contexts were first implemented as microtheories in the famed CYC common sense knowledge base (Guha 1991). However, while in CYC local microtheories were a choice, in contemporary settings like the semantic web the notion of local, distributed knowledge is a must. Modern architectures impose highly scattered, heterogeneous knowledge fragments, which a central reasoner is not able to deal with. Copyright c 2004, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. This engenders a high demand for distributed, contextual reasoning procedures. However, apart from few exceptions (Weyhrauch 1980; Massacci 1996), a general approach towards the automation of contextual reasoning has so far rarely been pursued. The pioneering work by Weyhrauch (1980) eventuated in an interactive multi-contextual theorem prover called FOL, which was later developed by Giunchiglia (1993b) into a more mature system called GETFOL. Both systems however, support automatic reasoning within a single context only. Cross contextual reasoning is left to their users. Massacci (1996) was the first to propose a completely automatic tableaux-based decision procedure for contextual reasoning. This procedure however, leaves open a substantial number of efficiency issues and moreover, only applies to propositional logic of context (PLC). We propose an automatic decision procedure called CSAT that computes satisfiability in multi-context systems (MCS). Furthermore, as MCS has recently been proven strictly more general than PLC (Bouquet & Serafini 2004), we show that CSAT can be applied to settle satisfiability in PLC as well. The contribution of this paper, then, is threefold: CSAT is the first sound and complete decision procedure for propositional multi-context systems. CSAT is the first SAT-based decision procedure for contextual reasoning in general, and as such improves (in terms of complexity) both on Massacci’s tableaux-based procedure for PLC, and on implicit results (based on equivalence results with modal logics) for MCS obtained from (Serafini & Giunchiglia 2002). Our approach could be applied to enhance recent proposals towards a new partition-based reasoning paradigm (Amir & McIlraith 2000; 2004); compared to alternative formalisms, MCS allows for more expressive descriptions of interpartition (intercontextual) relations, and CSAT is deliberately designed to deal with this expressiveness. We proceed as follows. After defining propositional multi-context systems and their local model semantics, we explicate the contextual satisfiability problem and describe CSAT. Subsequently, we consider CSAT’s computational complexity, and conclude with a discussion of the pros and cons of our approach in comparison with similar ones. Multi-Context Systems A simple illustration of the intuitions underlying MCS/LMS is provided by the so-called “magic box” example (Ghidini & Giunchiglia 2001), depicted below.