The CIFF Proof Procedure for Abductive Logic Programming with Constraints: Theory, Implementation and Experiments

We present the CIFF proof procedure for abductive logic programming with constraints, and we prove its correctness. CIFF is an extension of the IFF proof procedure for abductive logic programming, relaxing the original restrictions over variable quantification (allowedness conditions) and incorporating a constraint solver to deal with numerical constraints as in constraint logic programming. Finally, we describe the CIFF system, comparing it with state of the art abductive systems and answer set solvers and showing how to use it to program some applications. (To appear in Theory and Practice of Logic Programming - TPLP)

A Generic Framework for Reasoning about Dynamic Networks of Infinite-State Processes

We propose a framework for reasoning about unbounded dynamic networks of infinite-state processes. We propose Constrained Petri Nets (CPN) as generic models for these networks. They can be seen as Petri nets where tokens (representing occurrences of processes) are colored by values over some potentially infinite data domain such as integers, reals, etc. Furthermore, we define a logic, called CML (colored markings logic), for the description of CPN configurations. CML is a first-order logic over tokens allowing to reason about their locations and their colors. Both CPNs and CML are parametrized by a color logic allowing to express constraints on the colors (data) associated with tokens. We investigate the decidability of the satisfiability problem of CML and its applications in the verification of CPNs. We identify a fragment of CML for which the satisfiability problem is decidable (whenever it is the case for the underlying color logic), and which is closed under the computations of post and pre images for CPNs. These results can be used for several kinds of analysis such as invariance checking, pre-post condition reasoning, and bounded reachability analysis.Comment: 29 pages, 5 tables, 1 figure, extended version of the paper published in the the Proceedings of TACAS 2007, LNCS 442

Satisfiability of CTL* with constraints

We show that satisfiability for CTL* with equality-, order-, and modulo-constraints over Z is decidable. Previously, decidability was only known for certain fragments of CTL*, e.g., the existential and positive fragments and EF.Comment: To appear at Concur 201

Independence in computable algebra

We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and difference closed fields with the relevant notions of independence. To cover these classes of structures we introduce a new technique of safe extensions that was not necessary for the previously known results of this kind. We will then apply our techniques to derive new corollaries on the number of computable presentations of these structures. The condition also implies classical and new results on vector spaces, algebraically closed fields, torsion-free abelian groups and Archimedean ordered abelian groups.Comment: 24 page

The Tree Width of Separation Logic with Recursive Definitions

Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current results report on techniques to decide satisfiability and validity of entailments for Separation Logic(s) over lists (possibly with data). In this paper we establish a more general decidability result. We prove that any Separation Logic formula using rather general recursively defined predicates is decidable for satisfiability, and moreover, entailments between such formulae are decidable for validity. These predicates are general enough to define (doubly-) linked lists, trees, and structures more general than trees, such as trees whose leaves are chained in a list. The decidability proofs are by reduction to decidability of Monadic Second Order Logic on graphs with bounded tree width.Comment: 30 pages, 2 figure

Query Rewriting and Optimization for Ontological Databases

Ontological queries are evaluated against a knowledge base consisting of an extensional database and an ontology (i.e., a set of logical assertions and constraints which derive new intensional knowledge from the extensional database), rather than directly on the extensional database. The evaluation and optimization of such queries is an intriguing new problem for database research. In this paper, we discuss two important aspects of this problem: query rewriting and query optimization. Query rewriting consists of the compilation of an ontological query into an equivalent first-order query against the underlying extensional database. We present a novel query rewriting algorithm for rather general types of ontological constraints which is well-suited for practical implementations. In particular, we show how a conjunctive query against a knowledge base, expressed using linear and sticky existential rules, that is, members of the recently introduced Datalog+/- family of ontology languages, can be compiled into a union of conjunctive queries (UCQ) against the underlying database. Ontological query optimization, in this context, attempts to improve this rewriting process so to produce possibly small and cost-effective UCQ rewritings for an input query.Comment: arXiv admin note: text overlap with arXiv:1312.5914 by other author