Deciding Second-order Logics using Database Evaluation Techniques

We outline a novel technique that maps the satisfiability problems of second-order logics, in particular WSnS (weak monadic second-order logic with n successors), S1S (monadic second-order logic with one successor), and of μ-calculus, to the problem of query evaluation of Complex-value Datalog queries. In this dissertation, we propose techniques that use database evaluation and optimization techniques for automata-based decision procedures for the above logics. We show how the use of advanced implementation techniques for Deductive databases and for Logic Programs, in particular the use of tabling, yields a considerable improvement in performance over more traditional approaches. We also explore various optimizations of the proposed technique, in particular we consider variants of tabling and goal reordering. We then show that the decision problem for S1S can be mapped to the problem of query evaluation of Complex-value Datalog queries. We explore optimizations that can be applied to various types of formulas. Last, we propose analogous techniques that allow us to approach μ-calculus satisfiability problem in an incremental fashion and without the need for re-computation. In addition, we outline a top-down evaluation technique to drive our incremental procedure and propose heuristics that guide the problem partitioning to reduce the size of the problems that need to be solved

An Incremental Technique for Automata-based Decision Procedures

Abstract. Automata-based decision procedures commonly achieve optimal complexity bounds. However, in practice, they are often outperformed by sub-optimal (but more local-search based) techniques, such as tableaux, on many practical reasoning problems. This discrepancy is often the result of automata-style techniques global approach to the problem and the consequent need for constructing an extremely large automaton. This is in particular the case when reasoning in theories consisting of large number of relatively simple formulas, such as descriptions of database schemes, is required. In this paper, we propose techniques that allow us to approach a µ-calculus satisfiability problem in an incremental fashion and without the need for re-computation. In addition, we also propose heuristics that guide the problem partitioning in a way that is likely to reduce the size of the problems that need to be solved.

Logic Programming Approach to Automata-based Decision Procedures

Abstract. We propose a novel technique that maps decision problems in WS1S (weak monadic second-order logic with n successors) to the problem of query evaluation of Complex-value Datalog queries. We then show how the use of advanced implementation techniques for Logic Programs, in particular the use of tabling in the XSB system, yields a considerable improvement in performance over more traditional approaches. We also explore various optimizations of the proposed technique based on variants of tabling and goal reordering. Although our primary focus is on WS1S, it is straightforward to adapt our approach for other logics with existing automata-theoretic decision procedures, for example WS2S.

Towards a scalable, pragmatic knowledge representation language for the web

Abstract. A basic cornerstone of the Semantic Web are formal languages for describing resources in a clear and unambiguous way. Logical underpinnings facilitate automated reasoning about distributed knowledge on the Web and thus make it possible to derive only implicitly available information. Much research is geared to advancing very expressive formalisms that add increasingly complex modelling constructs. However, this increase in language expressivity is often intrinsically linked to higher computational cost and often leads to formalisms that have high theoretical complexity and that are difficult to implement efficiently. In contrast, reasoning in the context of the Web has a distinct set of requirements, namely inference systems that can scale to planetary-size datasets. A reduced level of expressivity is often sufficient for many practical scenarios and crucially, absolutely necessary when reasoning with such massive datasets. These requirements have been acknowledged by active research towards more lightweight formalisms and also by industrial implementations that often implement only tractable subsets of existing standards. In this paper we aim to explore this trend and formulate a basic language, called L2, layered upon RDF as the data-model, that is inherently tractable, easy to implement on common rule engines and motivated by pragmatic considerations concerning the use of language constructs and the means to implement them

Deciding Weak Monadic Second-order Logics

Abstract In this paper we propose to use techniques developed for query evaluation of Complex-value Datalog queries for determining satisfiability of WS1S and WS2S formulae. This in turn can serve as a decision procedure for Description Logics for which embeddings into WS1S and WS2S have been proposed recently. We show that the use of database query evaluation techniques--in particular the Magic Set rewriting of Datalog queries--can considerably improve the performance of automata-based reasoners such as the MONA system

Defining the Features of the WSML-DL v2.0 Language

In order to automate tasks such as location and composition, Semantic Web Services must be described in a well-defined formal language. The Web Services Modeling Language (WSML) is based on the conceptual model of the Web Service Modeling Ontology (WSMO) and as such can be used for modeling Web services, ontologies, and related aspects. WSML is actually a family of several language variants, each of which is based upon a different logical formalism. The family of languages is unified under one syntactic umbrella, with a concrete syntax for modeling ontologies. This deliverable, along with others, defines an updated version of the WSML language stack, in order to bring it in line with the scalability requirements of reasoning in SOA4All and realign it with new research results and others standards. Thus, this document describes WSML-DL v2.0, a WSML language variant of the Description Logics paradigm featuring a favorable trade-off between expressivity and scalability. By capturing the semantics of the ELP knowledge representation formalism, the updated WSML-DL variant greatly improves scalability and lends itself to evaluation using rule-based reasoners