Synchronous set relations in rewriting logic

This paper presents a mathematical foundation and a rewriting logic infrastructure for the execution and property verification of synchronous set relations. The mathematical foundation is given in the language of abstract set relations. The infrastructure, which is written in the Maude system, enables the synchronous execution of a set relation provided by the user. By using the infrastructure, algorithm verification techniques such as reachability analysis and model checking, already available in Maude for traditional asynchronous rewriting, are automatically available to synchronous set rewriting. In this way, set-based synchronous languages and systems such as those built from agents, components, or objects can be naturally specified and simulated, and are also amenable to formal verification in the Maude system. The use of the infrastructure and some of its Maude-based verification capabilities are illustrated with an executable operational semantics of the Plan Execution Interchange Language (PLEXIL), a synchronous language developed by NASA to support autonomous spacecraft operations.     

Equational rules for rewriting logic

In addition to equations and rules, we introduce equational rules that are oriented while having an equational interpretation. Correspondence between operational behavior and intended semantics is guaranteed by a property of coherence, which can be checked by examination of critical pairs and linearity conditions. We present applications of this theory to three examples where the rewrite relation is interpreted, respectively, as equality, transition and deduction.     

The rewriting logic semantics project

Rewriting logic is a flexible and expressive logical framework that unifies algebraic denotational semantics and structural operational semantics (SOS) in a novel way, avoiding their respective limitations and allowing succinct semantic definitions. The fact that a rewrite logic theory’s axioms include both equations and rewrite rules provides a useful “abstraction dial” to find the right balance between abstraction and computational observability in semantic definitions. Such semantic definitions are directly executable as interpreters in a rewriting logic language such as Maude, whose generic formal tools can be used to endow those interpreters with powerful program analysis capabilities.     

Maude: specification and programming in rewriting logic

Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude.     

A rewriting logic approach to operational semantics

This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: big-step and small-step structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, continuation-based semantics, and the chemical abstract machine. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a one-to-one correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or pre-impose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles.     

Quantifier-free logic for nondeterministic theories

We develop a quantifier-free logic for deriving consequences of multialgebraic theories. Multialgebras are used as models for nondeterminism in the context of algebraic specifications. They are many sorted algebras with set-valued operations. Formulae are sequents over atoms allowing one to state set-inclusion or identity of 1-element sets (determinacy). We introduce a sound and weakly complete Rasiowa–Sikorski (R–S) logic for proving multialgebraic tautologies. We then extend this system for proving consequences of specifications based on translation of finite theories into logical formulae. Finally, we show how such a translation may be avoided—introduction of the specific cut rules leads to a sound and strongly complete Gentzen system for proving directly consequences of specifications. Besides giving examples of the general techniques of R–S and the specific cut rules, we improve the earlier logics for multialgebras by providing means to handle empty carriers (as well as empty result-sets) without the use of quantifiers, and to derive consequences of theories without translation into another format and without using general cut.     

A rewriting logic framework for operational semantics of membrane systems

Existing results in membrane computing refer mainly to P systems’ characterization of Turing computability, also to some polynomial solutions to NP-complete problems by using an exponential workspace created in a “biological way”. In this paper we define an operational semantics of a basic class of P systems, and give two implementations of the operational semantics using rewriting logic. We present some results regarding these implementations, including two operational correspondence results, and discuss why these implementations are relevant in order to take advantage of good features of both structural operational semantics and rewriting logic.     

粗糙逻辑中理论相容性的拓扑刻画

有关文献将计量化方法应用于粗糙逻辑之中,建立起了用以处理近似推理问题的粗糙逻辑度量空间理论。拟借助于粗糙逻辑度量空间理论,从拓扑学的角度给出粗糙逻辑理论相容性的等价刻画。     

Simulation and analysis of MultEcore multilevel models based on rewriting logic

Software and Systems Modeling - Multilevel modelling (MLM) approaches make it possible for designers and modellers to work with an unlimited number of abstraction levels when specifying...     

Graph theoretical structures in logic programs and default theories

In this paper we present a graph representation of logic programs and default theories. We show that many of the semantics proposed for logic programs with negation can be expressed in terms of notions emerging from graph theory, establishing in this way a link between the fields. Namely the stable models, the partial stable models, and the well-founded semantics correspond respectively to the kernels, semikernels and the initial acyclic part of an associated graph. This link allows us to consider both theoretical (existence, uniqueness) and computational problems (tractability, algorithms, approximations) from a more abstract and rather combinatorial point of view. It also provides a clear and intuitive understanding about how conflicts between rules are resolved within the different semantics. Furthermore, we extend the basic framework developed for logic programs to the case of Default Logic by introducing the notions of partial, deterministic and well-founded extensions for default theories. These semantics capture different ways of reasoning with a default theory.     

Representing the MSR cryptoprotocol specification language in an extension of rewriting logic with dependent types

This paper presents a shallow and efficient embedding of the security protocol specification language MSR into an extension of rewriting logic with dependent types. The latter is an instance of the open calculus of constructions which integrates key concepts from equational logic, rewriting logic, and type theory. MSR is based on a form of first-order multiset rewriting extended with existential name generation and a flexible type infrastructure centered on dependent types with subsorting. The encoding presented in this paper has served as the basis for the implementation of an MSR specification and analysis environment using the first-order rewriting engine Maude.     

Abduction in logic programming: A new definition and an abductive procedure based on rewriting

A long outstanding problem for abduction in logic programming has been on how minimality might be defined. Without minimality, an abductive procedure is often required to generate exponentially many subsumed explanations for a given observation. In this paper, we propose a new definition of abduction in logic programming where the set of minimal explanations can be viewed as a succinct representation of the set of all explanations. We then propose an abductive procedure where the problem of generating explanations is formalized as rewriting with confluent and terminating rewrite systems. We show that these rewrite systems are sound and complete under the partial stable model semantics, and sound and complete under the answer set semantics when the underlying program is so-called odd-loop free. We discuss an application of abduction in logic programming to a problem in reasoning about actions and provide some experimental results.     

Specifying causality in action theories: a default logic approach

Recent research on reasoning about action has shown that the traditional logic form of domain constraints is problematic to represent ramifications of actions that are related to causality of domains. To handle this problem properly, as proposed by some researchers, it is necessary to describe causal relations of domains explicitly in action theories. In this paper, we address this problem from a new point of view. Specifically, unlike other researchers viewing causal relations as some kind of inference rules, we distinguish causal relations between defeasible and non-defeasible cases. It turns out that a causal theory in our formalism can be specified by using Reiter's default logic. Based on this idea, we propose a causality-based minimal change approach for representing effects of actions, and argue that our approach provides more plausible solutions for the ramification and qualification problems compared with other related work. We also describe a logic programming approximation to compute causal theories of actions which provides an implementational basis for our approach.     

命题模糊逻辑系统中有限理论的弱相容度

推广了命题模糊逻辑系统中有限理论相容性的概念。以理论Г是否同时推出命题A和命题┐A为基准点引进了有限理论弱相容度的新概念,讨论了其性质,并给出了判定它大小的一系列准则。     

二值命题逻辑理论的结论类型和分类

以公式真度为基础,研究了二值命题逻辑系统中有限理论逻辑推出的结论类型和分别基于公式真度以及逻辑等价的分类问题,给出了分类定理以及同一理论结论的相似度的一个下界。     

Nominal rewriting

Nominal rewriting is based on the observation that if we add support for α-equivalence to first-order syntax using the nominal-set approach, then systems with binding, including higher-order reduction schemes such as λ-calculus beta-reduction, can be smoothly represented. Nominal rewriting maintains a strict distinction between variables of the object-language (atoms) and of the meta-language (variables or unknowns). Atoms may be bound by a special abstraction operation, but variables cannot be bound, giving the framework a pronounced first-order character, since substitution of terms for variables is not capture-avoiding. We show how good properties of first-order rewriting survive the extension, by giving an efficient rewriting algorithm, a critical pair lemma, and a confluence theorem for orthogonal systems.     

New trends in recognizing experimental drives: fuzzy logic andformal language theories

Drive systems today determine the productivity and quality of industrial processes. However, they exhibit considerable complexities related with their behavior as large uncertainties at a structure and parameter levels, multidimensionality, and strong mutual interactions. This paper aims to analyze common features, and the potential, but also the drawbacks that fuzzy logic and formal language theories show when used for recognition of patterns in experimental drives. Two prototype systems are used: an electrohydraulic drive and an induction motor drive. We underline the similarities and various aspects of the recognition methodologies, despite their use on different systems. A set of experimental learning situations with critical effects on their performance are presented and discussed     

A formal approach to the specification and the behavior validation of real-time systems based on rewriting logic

Design of real time and concurrent systems requires formal approaches in order to facilitate verification and validation at each step. Methods based on formal logic have been previously suggested but they often work only in a specific domain and are generally only possible with specialized users. In an attempt to overcome these two restrictions, this paper proposes a method based on rewriting logic. A grounding in theory is not a prerequisite for users. The method integrates modularity and abstraction and follows the main principles of an object-oriented approach. Different tools are available: a graphical editor for the specification of the structure and the behavior of the objects, an inference engine for rule validation and a generator of prototypes.