Contributions to the semantics of logic perpetual processes

Summary Logic perpetual processes (logic programs with infinite data structures) have been given several formal (operational and fixpoint) semantics. In this paper, we compare the various semantics and define a formal characterization of a least fixpoint semantics, which is based on a modified version of the logic programs and which is satisfactory for a large class of logical perpetual processes. Our results show that all the proposed fixpoint semantics are not equivalent to the operational semantics and suggest an improvement of the least fixpoint approach.     

On the verification of finite failure

In Gori [An abstract interpretation framework to reason on finite failure and other properties of finite and infinite computations, Theoret. Comput. Sci. 290(1) (2003) 863-936] a new fixpoint semantics which correctly models finite failure has been defined. This semantics is And-compositional, compositional w.r.t. instantiation and is based on a co-continuous operator. Based on this fixpoint semantics a new inductive method able to verify a program w.r.t. the property of finite failure can be defined. In this paper we show how Ferrand's approach, using both a least fixpoint and greatest fixpoint semantics, can be adapted to finite failure. The verification method is not effective. Therefore, we consider an approximation from above and an approximation from below of our semantics, which give two different finite approximations. These approximations are used for effective program verification.     

Merging graph-based and rule-based computation: The language G-Log

In this paper we discuss the merging of two different computation paradigms: the fixpoint computation for deductive databases and the pattern-matching computation for graph-based languages. We show how these paradigms can be combined on the example of the declarative, graph-based, database query language G-Log. A naive algorithm to compute G-Log programs turns out to be very inefficient. However, we also present a backtracking fixpoint algorithm for Generative G-Log, a syntactical sublanguage of G-Log that, like G-Log, is non-deterministic complete. This algorithm is considerably more efficient, and reduces to the standard fixpoint computation for a sublanguage of Generative G-Log that is a graphical equivalent of Datalog. The paper also studies some interesting properties like satisfiability and triviality, that are undecidable for full G-Log and turn out to be decidable for sufficiently general classes of Generative G-Log programs.     

On stratified disjunctive programs

We address the problem of a consistent fixpoint semantics for general disjunctive programs restricted to stratifiable programs which do not recurse through negative literals. We apply the nonmonotonic fixpoint theory developed by Apt, Blair and Walker to a closure operatorT ^c and develop a fixpoint semantics for stratified disjunctive programs. We also provide an iterative definition for negation, called the Generalized Closed World Assumption for Stratified programs (GCWAS), and show that our semantics captures this definition. We develop a model-theoretic semantics for stratified disjunctive programs and show that the least state characterized by the fixpoint semantics corresponds to a stable-state defined in a manner similar to the stable-models of Gelfond and Lifschitz. We also discuss a weaker stratification semantics for general disjunctive programs based on the Weak Generalized Closed World Assumption.     

Symbolic systems,explicit properties: on hybrid approaches for LTL symbolic model checking

In this work we study hybrid approaches to LTL symbolic model checking; that is, approaches that use explicit representations of the property automaton, whose state space is often quite manageable, and symbolic representations of the system, whose state space is typically exceedingly large. We compare the effects of using, respectively, (i) a purely symbolic representation of the property automaton, (ii) a symbolic representation, using logarithmic encoding, of explicitly compiled property automaton, and (iii) a partitioning of the symbolic state space according to an explicitly compiled property automaton. We apply this comparison to three model-checking algorithms: the doubly-nested fixpoint algorithm of Emerson and Lei, the reduction of emptiness to reachability of Biere et al., and the singly-nested fixpoint algorithm of Bloem et al. for weak automata. The emerging picture from our study is quite clear, hybrid approaches outperform pure symbolic model checking, while partitioning generally performs better than logarithmic encoding. The conclusion is that the hybrid approaches benefit from state-of-the-art techniques in semantic compilation of LTL properties. Partitioning gains further from the fact that the image computation is applied to smaller sets of states.     

Control synthesis of timed discrete event systems based onpredicate invariance

In this paper, arc-timed Petri nets are used to model controlled real-time discrete event systems, and the control synthesis problem that designs a controller for a system to satisfy its given closed-loop behavior specification is addressed. For the problem with the closed-loop behavior specified by a state predicate, real-time control-invariant predicates are introduced, and a fixpoint algorithm to compute the unique extremal control-invariant subpredicate of a given predicate, key to the control synthesis, is presented. For the problem with the behavior specified by a labeled arc-timed Petri net, it is shown that the control synthesis problem can be transformed into one that synthesizes a controller for an induced arc-timed Petri net with a state predicate specification. The problem can then be solved by using the fixpoint algorithm as well. The algorithm involves conjunction and disjunction operations of polyhedral sets and can be algorithmically implemented, making automatic synthesis of controllers for real-time discrete event systems possible.     

Reexecution in abstract interpretation of Prolog

Logic programming, because of referential transparency, enjoys the property that a literal may be reexecuted finitely often without affecting the meaning of the program. This property, although not interesting computationally in general, can be exploited in abstract interpretation to improve the accuracy of the analysis, as noted by Bruynooghe in [6].We study reexecution from its theoretical foundations to its experimental evaluation. We define a new abstract semantics for Prolog, which incorporates the notion of reexecution, and we study its correctness and precision properties. A fixpoint algorithm to compute the abstract semantics is then presented. The accuracy and efficiency of the algorithm is evaluated experimentally on two abstract domains, a simple and an elaborate one, and compared with conventional approaches.The experimental results indicate that (1) reexecution can provide significant gains in accuracy at a very reasonable computation cost and that (2) reexecution on a simple domain is a versatile alternative to the standard approach on a more sophisticated domain.An extended abstract of this paper appeared in [29].     

Querying Weak Instances Under Extension Chase Semantics: A Complete Solution

The problem of computing windows using relational expressions has been solved only in certain cases in which the chase semantics and the extension chase semantics of the database coincide. However, the general problem of computing windows under either chase semantics or extension chase semantics, but without restrictions, remained an open problem. In this paper we present a complete solution of the general problem, under extension chase semantics. Our solution is complete in the sense that it does not require any assumption on the database scheme or on the database state. It follows that our approach subsumes previous approaches, and we exhibit cases in which our approach correctly computes the windows, while previous approaches fail to do so. Moreover, the efficiency of our approach lies in the fact that it uses only those relation schemes and only those functional dependencies that are necessary in the computation of windows. The main technique employed by our approach is a least fixpoint construction using the notion of cover (a cover being a set of relation schemes satisfying certain properties). The proposed technique can be implemented using relational algebra plus recursion.     

Fixing Zeno gaps

In computer science, fixpoints play a crucial role. Most often least and greatest fixpoints are sufficient. However, there are situations where other ones are needed. In this paper, we study, on an algebraic base, a special fixpoint of the function f(x)=a⋅x that describes infinite iteration of an element a. We show that the greatest fixpoint is too imprecise. Special problems arise if the iterated element contains the possibility of stepping on the spot (e.g. skip in a programming language) or if it allows Zeno behaviour. We present a construction for a fixpoint that captures these phenomena in a precise way. The theory is presented and motivated using an example from hybrid system analysis.     

基于逻辑程序的访问控制描述与推理

提出访问控制的逻辑描述方法,满足最小模型语义的条件(不含负逻辑),并分析访问控制逻辑程序中不动点的迭代计算方法。通过迭代计算,得到访问控制逻辑程序的最小Herbrand模型——Mp。使用基于逻辑程序的方法对访问控制策略进行了较为精确的推理。     

Bottom-up Evaluation of Datalog with Negation

Declarative semantics gives the meaning of a logic program in terms of properties,while the procedural semantics gives the meaning in terms of the execution or evaluation of the program.From the database point of view,the procedural semantics of the program is equally important.This paper focuses on the study of the bottom-up evaluation of the WFM semantics of datalog‘ programs.To compute the WFM,first,the stability transformation is revisited,and a new operator Op and its fixpoint are defined. Based on this,a fixpoint semantics,called oscillating fixpoint model semantics,is defined.Then,it is shown that for any datalog‘ program the oscillating fixpoint model is identical to its WFM.So,the oscillating fixpoint model can be viewed as an alternative (constructive) definition of WFM.The underlying operation (or transformation) for reaching the oscillating fixpoint provides a potential of bottom-up evaluation.For the sake of computational feasibility,the strongly range-restricted program is considered,and an algorithm used to compute the oscillating fixpoint is described.     

RFuzzy: Syntax, semantics and implementation details of a simple and expressive fuzzy tool over Prolog

We present the RFuzzy framework, a Prolog-based tool for representing and reasoning with fuzzy information. The advantages of our framework in comparison to previous tools along this line of research are its easy, user-friendly syntax, and its expressivity through the availability of default values and types.In this approach we describe the formal syntax, the operational semantics and the declarative semantics of RFuzzy (based on a lattice). A least model semantics, a least fixpoint semantics and an operational semantics are introduced and their equivalence is proven. We provide a real implementation that is free and available. (It can be downloaded from http://babel.ls.fi.upm.es/software/rfuzzy/.) Besides implementation details, we also discuss some actual applications using RFuzzy.     

Formalization of correctness of recursive definitions

We use the fixpoint approach to formalize the correctness of recursive definitions within the framework of first-order predicate calculus. Although the least fixpoint semantics is used, our results suggest some general methods of proving the correctness of recursive definitions without knowing their least fixpoints explicitly.     

Linearizing some recursive logic programs

We give a sufficient condition under which the least fixpoint of the equation X=a+f(X)X equals the least fixpoint of the equation X=a+f(a)X. We then apply that condition to recursive logic programs containing chain rules: we translate it into a sufficient condition under which a recursive logic program containing n⩾2 recursive calls in the bodies of the rules is equivalent to a linear program containing at most one recursive call in the bodies of the rules. We conclude with a discussion comparing our condition with the other approaches to linearization studied in the literature     

On Improving Backwards Verification of Timed Automata (Extended Abstract)

Verification techniques for Timed Automata [2] built in tools like Kronos [7] are based on the fixpoint calculus of an appropriate operator. In this work, we present different alternatives to calculate that fixpoint, which have direct impact in the number of iterations needed to converge.     

Results on the propositional μ-calculus

In this paper we define and study a propositional μ-calculus Lμ, which consists essentially of propositional modal logic with a least fixpoint operator. Lμ is syntactically simpler yet strictly more expressive than Propositional Dynamic Logic (PDL). For a restricted version we give an exponential-time decision procedure, small model property, and complete deductive system, theory subsuming the corresponding results for PDL.     

On the existence of optimal fixpoints

The concept of optimal fixpoint was introduced by Manna and Shamir [6, 7] in order to extract the maximum amount of “useful” information from a recursive definition. In this paper, we extend the concept of optimal fixpoint to arbitrary posets and investigate conditions which guarantee their existence. We prove that if a poset is chain-complete and has bounded joins, then every monotonic function has an optimal fixpoint. We also provide a sort of converse which generalizes a Theorem of A. Davis [2]. If a lower semilattice has bounded joins and every monotonic function has a fixpoint, then it is chain-complete.     

MRMOGA: a new parallel multi‐objective evolutionary algorithm based on the use of multiple resolutions

In this paper, we introduce MRMOGA (Multiple Resolution Multi‐Objective Genetic Algorithm), a new parallel multi‐objective evolutionary algorithm which is based on an injection island approach. This approach is characterized by adopting an encoding of solutions which uses a different resolution for each island. This approach allows us to divide the decision variable space into well‐defined overlapped regions to achieve an efficient use of multiple processors. Also, this approach guarantees that the processors only generate solutions within their assigned region. In order to assess the performance of our proposed approach, we compare it to a parallel version of an algorithm that is representative of the state‐of‐the‐art in the area, using standard test functions and performance measures reported in the specialized literature. Our results indicate that our proposed approach is a viable alternative to solve multi‐objective optimization problems in parallel, particularly when dealing with large search spaces. Copyright © 2006 John Wiley & Sons, Ltd.     

利用不动点求解子句逻辑推演的Petri网模型

文章研究了子句逻辑推演的Petri网模型表示和不动点求解方法.基于四值逻辑和冲突变迁的概念,可用Horn子句的Petri网模型方法来构造非Horn子句的Petri网模型.逻辑推演的基本方法之一就是寻找逻辑赋值的不动点.该文显示了一种基于Petri网模型的子句逻辑不动点求解算法,比现有算法更为有效.