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We report on an investigation aimed at identifying small fragments of set theory (typically, sublanguages of Multi-Level Syllogistic) endowed with polynomial-time satisfiability decision tests, potentially useful for automated proof verification. Leaving out of consideration the membership relator ∈ for the time being, in this paper we provide a complete taxonomy of the polynomial and the NP-complete fragments involving, besides variables intended to range over the von Neumann set-universe, the Boolean operators ∪ ∩ \, the Boolean relators ⊆, ⊈,=, ≠, and the predicates '• = Ø' and 'Disj(•, •)', meaning 'the argument set is empty' and 'the arguments are disjoint sets', along with their opposites '• ≠ Ø and '¬Disj(•, •)'. We also examine in detail how to test for satisfiability the formulae of six sample fragments: three sample problems are shown to be NP-complete, two to admit quadratic-time decision algorithms, and one to be solvable in linear time. [ABSTRACT FROM AUTHOR]

In this paper we present a methodology for introducing customizable metalogic features in logic-based knowledge representation and reasoning languages. The proposed approach is based on concepts of introspection and reflection previously introduced and discussed by various authors in relevant literature. This allows a knowledge engineer to specify enhanced reasoning engines by defining properties and meta-properties of relations as expressible for instance in OWL. We employ meta-level axiom schemata based upon a naming (reification) device. We propose general principles for extending the semantics of "host" formalisms accordingly. Consequently, suitable pre-defined libraries of properties can be made available, while user-defined new schemata are also allowed. We make the specific cases of Answer Set Programming (ASP) and Datalog±, where such features may be part of software engineering toolkits for these programming paradigms. On the one hand, concerning ASP, we extend the programming principles and practice to accommodate the proposed methodology, so as to perform meta-reasoning within the plain ASP semantics. The computational complexity of the resulting framework does not change. On the other hand, we show how metalogic features can significantly enrich Datalog± with minor changes to its operational semantics (provided in terms of "chase") and, also in this case, no additional complexity burden. [ABSTRACT FROM AUTHOR]

In this paper, we study an information flow security property for systems specified as terms of a quantitative Markovian process algebra, namely the Performance Evaluation Process Algebra (PEPA). We propose a quantitative extension of the Non-Interference property used to secure systems from the functional point view by assuming that the observers are able to measure also the timing properties of the system, e.g., the response time of certain actions or its throughput. We introduce the notion of Persistent Stochastic Non-Interference (PSNI) based on the idea that every state reachable by a process satisfies a basic Stochastic Non-Interference (SNI) property. The structural operational semantics of PEPA allows us to give two characterizations of PSNI: one based on a bisimulation-like equivalence relation inducing a lumping on the underlying Markov chain, and another one based on unwinding conditions which demand properties of individual actions. These two different characterizations naturally lead to efficient methods for the verification and construction of secure systems. A decision algorithm for PSNI is presented and an application of PSNI to a queueing system is discussed. [ABSTRACT FROM AUTHOR]

The axiom of elementary states the existence of a void set and the availability of an unordered pair formation operation. This axiom states that distinct sets cannot have precisely the same elements immediately after the extensionality axiom.

In this paper we present a methodology for introducing customizable metalogic features in logic-based knowledge representation and reasoning languages. The proposed approach is based on concepts of introspection and reflection previously introduced and discussed by various authors in relevant literature. This allows a knowledge engineer to specify enhanced reasoning engines by defining properties and meta-properties of relations as expressible for instance in OWL. We employ meta-level axiom schemata based upon a naming (reification) device. We propose general principles for extending the semantics of "host" formalisms accordingly. Consequently, suitable pre-defined libraries of properties can be made available, while user-defined new schemata are also allowed. We make the specific cases of Answer Set Programming (ASP) and Datalog±, where such features may be part of software engineering toolkits for these programming paradigms. On the one hand, concerning ASP, we extend the programming principles and practice to accommodate the proposed methodology, so as to perform meta-reasoning within the plain ASP semantics. The computational complexity of the resulting framework does not change. On the other hand, we show how metalogic features can significantly enrich Datalog± with minor changes to its operational semantics (provided in terms of "chase") and, also in this case, no additional complexity burden. [ABSTRACT FROM AUTHOR]

We report on an investigation aimed at identifying small fragments of set theory (typically, sublanguages of Multi-Level Syllogistic) endowed with polynomial-time satisfiability decision tests, potentially useful for automated proof verification. Leaving out of consideration the membership relator ∈ for the time being, in this paper we provide a complete taxonomy of the polynomial and the NP-complete fragments involving, besides variables intended to range over the von Neumann set-universe, the Boolean operators ∪ ∩ \, the Boolean relators ⊆, ⊈,=, ≠, and the predicates '• = Ø' and 'Disj(•, •)', meaning 'the argument set is empty' and 'the arguments are disjoint sets', along with their opposites '• ≠ Ø and '¬Disj(•, •)'. We also examine in detail how to test for satisfiability the formulae of six sample fragments: three sample problems are shown to be NP-complete, two to admit quadratic-time decision algorithms, and one to be solvable in linear time. [ABSTRACT FROM AUTHOR]