Alvaro del Val

Tractable databases: how to make propositional unit resolution complete through compilation

We present procedures to compile any propositional clausal database σ into a logically equivalent “compiled” database σ * such that. for any clause C , σ |= C if and only if there is a unit refutation of σ * U C . It follows that once the compilation process is complete any query about the logical consequences of σ can be correctly answered in time linear in the sum of the sizes of σ * and the query. The compiled database σ * is for all but one of the procedures a subset of the set PI (σ) of prime implicates of σ, but σ * can be exponentially smaller than PI (σ). Of independent interest, we prove the equivalence of unit-refutability with two restrictions of resolution, and provide a new sufficient condition for unit refutation completeness, thus identifying a new class of tractable theories, one which is of interest to abduction problems as well. Finally, we apply the results to the design of a complete LTMS.

A Unified View of Belief Revision and Update

Belief revision and belief update have been considered as two distinct types of belief mod-iication. In this paper, we show that both can be captured within an uniied formalism, in which revision is encoded as update of the mental state. Speciically, we show that the framework for belief update presented in 6, 7] can be used to capture revision as well, by extending the underlying language to include explicit representations of the agents beliefs. The resulting framework allows for the deenition of a wide variety of revision operators. These include, in particular, all the AGM operators, for which we provide a representation theorem.

Deriving properties of belief update from theories of action (II)

AbstractWe present an approach to database update as a form of non monotonic temporal reasoning, the main idea of which is the (circumscriptive) minimization of changes with respect to a set of facts declared “persistent by default”. The focus of the paper is on the relation between this approach and the update semantics recently proposed by Katsuno and Mendelzon. Our contribution in this regard is twofold: We prove a representation theorem for KM semantics in terms of a restricted subfamily of the operators defined by our construction.We show how the KM semantics can be generalized by relaxing our construction in a number of ways, each justified in certain intuitive circumstances and each corresponding to one specific postulate. It follows that there are reasonable update operators outside the KM family.Our approach is not dependent for its plausibility on this connection with KM semantics. Rather, it provides a relatively rich and flexible framework in which the frame and ramification problems can be solved in a systematic way by reasoning about default persistence of facts.

Redundant modeling for The QuasiGroup Completion Problem

The Quasigroup Completion Problem (QCP) is a very challenging benchmark among combinatorial problems, and the focus of much recent interest in the area of constraint programming. [5] reports that QCPs of order 40 could not be solved by pure constraint programming approaches, but could sometimes be solved by hybrid approaches combining constraint programming with mixed integer programming techniques from operations research. In this paper, we show that the pure constraint satisfaction approach can solve many problems of order 45 in the transition phase, which corresponds to the peak of difficulty. Our solution combines a number of known ideas -the use of redundant modeling [3] with primal and dual models of the problem connected by channeling constraints [13] - with some novel aspects, as well as a new and very effective value ordering heuristic.

Non monotonic reasoning and belief revision: syntactic, semantic, foundational and coherence approaches

ABSTRACT The major approaches to belief revision and non monotonic reasoning proposed in the literature differ along a number of dimensions, including whether they are “syntax- based” or “semantic-based”, “foundational” or “coherentist”, “consistence-restoring” or “inconsistency-tolerant”. Our contribution towards clarifying the connections between these various approaches is threefold: •We show that the two main approaches to belief revision, the foundations and coherence theories, are mathematically equivalent, thus answering a question left open in [Gar90, Doy92], The distinction between syntax-based approaches to revision and approaches based on (semantic) preferential structures falls along similar lines, and their expressive equivalence is a consequence of this result. •We formally clarify the connection between belief revision and non monotonic reasoning, in a particularly simple way which also throws light on the connection between consistence- restoring and reasoning-from-inconsistency approaches...

Simplifying Binary Propositional Theories into Connected Components Twice as Fast

Binary propositional theories, composed of clauses with at most two literals, are one of the most interesting tractable subclasses of the satisfiability problem. We present two hybrid simplification algorithms for binary theories, which combine the unit-resolution-based 2SAT algorithm BinSat [9] with refined versions of the classical strongly connected components (SCC) algorithm of [1]. We show empirically that the algorithms are considerably faster than other SCC-based algorithms, and have greater simplifying power, as they combine detection of entailed literals with identification of SCCs, i.e. sets of equivalent literals. By developing faster simplification algorithms we hope to contribute to attempts to integrate simplification of binary theories within the search phase of general SAT solvers.

Scheduling social tournaments

Tournament scheduling problems arise in many practical applications and their highly symmetric and combinatorial nature makes them particularly challenging for search algorithms. This research generalizes the modeling and local search approach proposed in [1] in order to schedule some challenging, real-life, social tournaments. The approach also schedules other challenging, social tournaments. Results can be found in the web version of this abstract.

Approximate Update of Logical Databases

In [6, 7], we presented syntactic characterizations and algorithms for computing the result of updating and revising a logical database under various approaches proposed in the literature. In this paper we focus on the design of versions of these algorithms able to provide an approximate answer if interrupted before completion. We use the PMA approach to update [18] as the main example, but the results readily generalize to a wide family of update operators.