A Neutrosophic Description Logic

Description Logics (DLs) are appropriate, widely used, logics for managing structured knowledge. They allow reasoning about individuals and concepts, i.e. set of individuals with common properties. Typically, DLs are limited to dealing with crisp, well defined concepts. That is, concepts for which the problem whether an individual is an instance of it is yes/no question. More often than not, the concepts encountered in the real world do not have a precisely defined criteria of membership: we may say that an individual is an instance of a concept only to a certain degree, depending on the individual's properties. The DLs that deal with such fuzzy concepts are called fuzzy DLs. In order to deal with fuzzy, incomplete, indeterminate and inconsistent concepts, we need to extend the fuzzy DLs, combining the neutrosophic logic with a classical DL. In particular, concepts become neutrosophic (here neutrosophic means fuzzy, incomplete, indeterminate, and inconsistent), thus reasoning about neutrosophic concepts is supported. We'll define its syntax, its semantics, and describe its properties.Comment: 18 pages. Presented at the IEEE International Conference on Granular Computing, Georgia State University, Atlanta, USA, May 200

Reasoning in the Bernays-Schönfinkel-Ramsey Fragment of Separation Logic

International audienceSeparation Logic (SL) is a well-known assertion language used in Hoare-style modular proof systems for programs with dynamically allocated data structures. In this paper we investigate the fragment of first-order SL restricted to the Bernays-Schönfinkel-Ramsey quantifier prefix ∃ * ∀ * , where the quantified variables range over the set of memory locations. When this set is uninterpreted (has no associated theory) the fragment is PSPACE-complete, which matches the complexity of the quantifier-free fragment [7]. However, SL becomes undecid-able when the quantifier prefix belongs to ∃ * ∀ * ∃ * instead, or when the memory locations are interpreted as integers with linear arithmetic constraints, thus setting a sharp boundary for decidability within SL. We have implemented a decision procedure for the decidable fragment of ∃ * ∀ * SL as a specialized solver inside a DPLL(T) architecture, within the CVC4 SMT solver. The evaluation of our implementation was carried out using two sets of verification conditions, produced by (i) unfolding inductive predicates, and (ii) a weakest precondition-based verification condition generator. Experimental data shows that automated quantifier instantiation has little overhead, compared to manual model-based instantiation

Answering SPARQL queries modulo RDF Schema with paths

SPARQL is the standard query language for RDF graphs. In its strict instantiation, it only offers querying according to the RDF semantics and would thus ignore the semantics of data expressed with respect to (RDF) schemas or (OWL) ontologies. Several extensions to SPARQL have been proposed to query RDF data modulo RDFS, i.e., interpreting the query with RDFS semantics and/or considering external ontologies. We introduce a general framework which allows for expressing query answering modulo a particular semantics in an homogeneous way. In this paper, we discuss extensions of SPARQL that use regular expressions to navigate RDF graphs and may be used to answer queries considering RDFS semantics. We also consider their embedding as extensions of SPARQL. These SPARQL extensions are interpreted within the proposed framework and their drawbacks are presented. In particular, we show that the PSPARQL query language, a strict extension of SPARQL offering transitive closure, allows for answering SPARQL queries modulo RDFS graphs with the same complexity as SPARQL through a simple transformation of the queries. We also consider languages which, in addition to paths, provide constraints. In particular, we present and compare nSPARQL and our proposal CPSPARQL. We show that CPSPARQL is expressive enough to answer full SPARQL queries modulo RDFS. Finally, we compare the expressiveness and complexity of both nSPARQL and the corresponding fragment of CPSPARQL, that we call cpSPARQL. We show that both languages have the same complexity through cpSPARQL, being a proper extension of SPARQL graph patterns, is more expressive than nSPARQL.Comment: RR-8394; alkhateeb2003

First-order theory of subtyping constraints

We investigate the first-order theory of subtyping constraints. We show that the first-order theory of non-structural subtyping is undecidable, and we show that in the case where all constructors are either unary or nullary, the first-order theory is decidable for both structural and non-structural subtyping. The decidability results are shown by reduction to a decision problem on tree automata. This work is a step towards resolving long-standing open problems of the decidability of entailment for non-structural subtyping

Complexity of validity for propositional dependence logics

We study the validity problem for propositional dependence logic, modal dependence logic and extended modal dependence logic. We show that the validity problem for propositional dependence logic is NEXPTIME-complete. In addition, we establish that the corresponding problem for modal dependence logic and extended modal dependence logic is NEXPTIME-hard and in NEXPTIME^NP.Comment: In Proceedings GandALF 2014, arXiv:1408.556

On Algorithms and Complexity for Sets with Cardinality Constraints

Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate properties: relationships between the typestates of objects can be expressed as subset and disjointness relations on sets, and elements of sets can be represented as sets of cardinality one. Motivated by these applications, this paper presents new algorithms and new complexity results for constraints on sets and their cardinalities. We study several classes of constraints and demonstrate a trade-off between their expressive power and their complexity. Our first result concerns a quantifier-free fragment of Boolean Algebra with Presburger Arithmetic. We give a nondeterministic polynomial-time algorithm for reducing the satisfiability of sets with symbolic cardinalities to constraints on constant cardinalities, and give a polynomial-space algorithm for the resulting problem. In a quest for more efficient fragments, we identify several subclasses of sets with cardinality constraints whose satisfiability is NP-hard. Finally, we identify a class of constraints that has polynomial-time satisfiability and entailment problems and can serve as a foundation for efficient program analysis.Comment: 20 pages. 12 figure