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.     

Interpreters from functions and grammars

The addition of context free grammar rules to a functional language simplifies the construction of interpreters from denotational semantic language definitions. Functional abstraction over grammar rules enables the specification and processing of context sensitive language syntax aspects in a functional style.     

Multi-engine Horn Clause Prolog

We extend Horn Clause Prolog with two new primitives, new_engine (+Goal, +Answer, -Engine) and new_answer(+Engine, -Answer) for creating and exploring answer spaces of multiple interpreters (engines). We show that despite its ontological parsimony, the resulting language is comparable in practical expressiveness with conventional full Prolog, by allowing compact definitions for negation, if-then-else, all solution predicates, I/O and reflective meta-interpreters. While not really needed anymore as a workaround for the lack of expressiveness of pure Prolog, a form of dynamic database operations can be emulated as well, using the state of multiple engines. With multiple engines laying the foundation for multi-threaded execution models of logic programming languages, the surprising result that a minimal extension of Horn Clauses (with LD resolution) in fact bridges the gap to full Prolog, is significant as a basis for lightweight implementations of embedabble logic programming components. Our constructs have been used in the design of small footprint mobile code interpreters for a commercial multi-threaded agent programming language - Jinni - available from http://www.binnetcorp.com/Jinni”.     

Semantic foundations for generalized rewrite theories

Rewriting logic (RL) is a logic of actions whose models are concurrent systems. Rewrite theories involve the specification of equational theories of data and state structures together with a set of rewrite rules that model the dynamics of concurrent systems. Since its introduction, more than one decade ago, RL has attracted the interest of both theorists and practitioners, who have contributed in showing its generality as a semantic and logical framework and also as a programming paradigm. The experimentation conducted in these years has suggested that some significant extensions to the original definition of the logic would be very useful in practice. These extensions may develop along several dimensions, like the choice of the underlying equational logic, the kind of side conditions allowed in rewrite rules and operational concerns for the execution of certain rewrites. In particular, the Maude system now supports subsorting and conditional sentences in the equational logic for data, and also frozen arguments to block undesired nested rewrites; moreover, it allows equality and membership assertions in rule conditions. In this paper, we give a detailed presentation of the inference rules, model theory, and completeness of such generalized rewrite theories. Our results provide a mathematical semantics for Maude, and a foundation for formal reasoning about Maude specifications.     

On the Relative Soundness of the Free Algebra Model for Public Key Encryption

Formal systems for cryptographic protocol analysis typically model cryptosystems in terms of free algebras. Modeling the behavior of a cryptosystem in terms of rewrite rules is more expressive, however, and there are some attacks that can only be discovered when rewrite rules are used. But free algebras are more efficient, and appear to be sound for “most” protocols. In [J. Millen, “On the freedom of decryption”, Information Processing Letters 86 (6) (June 2003) 329–333] Millen formalizes this intuition for shared key cryptography and provides conditions under which it holds; that is, conditions under which security for a free algebra version of the protocol implies security of the version using rewrite rules. Moreover, these conditions fit well with accepted best practice for protocol design. However, he left public key cryptography as an open problem. In this paper, we show how Millen's approach can be extended to public key cryptography, giving conditions under which security for the free algebra model implies security for the rewrite rule model. As in the case for shared key cryptography, our conditions correspond to standard best practice for protocol design.     

Reconfigurable control of robotized manufacturing cells

This paper investigates the field of manufacturing system control. The addressed subject is indeed very fascinating, due to the importance that it has reached in the last decades both at research and industrial level. On the other hand, it seems to the author that most of the complexity intrinsic to the subject itself relies on the different meanings or levels of abstraction that both the terms “manufacturing system” and “control” may symbolize. The presented research aims to face the topic in a concrete fashion, i.e., by developing a control software system for a specific, although easy to be generalized, robotized manufacturing cell. Two different development methodologies, from the conceptual design to the actual implementation, of a cell control system are presented and compared. The former, based on ladder logic diagrams, for a PLC controlled manufacturing cell; the latter, based on object-oriented modeling and programming techniques, for a PC controlled manufacturing cell. The analysis has been conducted considering the internal and external requirements of the manufacturing system, mostly driven by the contemporary industrial need of reconfigurable control systems, largely acknowledged as the critical key to succeed in the new era of mass customization.     

Oracle Semantics for Prolog

This paper proposes to specify semantic definitions for logic programming languages such as Prolog in terms of an oracle which specifies the control strategy and identifies which clauses are to be applied to resolve a given goal. The approach is quite general. It can be applied to Prolog to specify both operational and declarative semantics as well as other logic programming languages. Previous semantic definitions for Prolog typically encode the sequential depth-first search of the language into various mathematical frameworks. Such semantics mimic a Prolog interpreter in the sense that following the "leftmost" infinite path in the computation tree excludes computation to the right of this path from being considered by the semantics. The basic idea in this paper is to abstract away from the sequential control of Prolog and to provide a declarative characterization of the clauses to apply to a given goal. The decision whether or not to apply a clause is viewed as a query to an oracle which is specified from within the semantics and reasoned about from outside. This approach results in simple and concise semantic definitions which are more useful for arguing the correctness of program transformations and providing the basis for abstract interpretations than previous proposals.     

Formal Proofs About Rewriting Using ACL2

We present an application of the ACL2 theorem prover to reason about rewrite systems theory. We describe the formalization and representation aspects of our work using the first-order, quantifier-free logic of ACL2 and we sketch some of the main points of the proof effort. First, we present a formalization of abstract reduction systems and then we show how this abstraction can be instantiated to establish results about term rewriting. The main theorems we mechanically proved are Newman's lemma (for abstract reductions) and Knuth–Bendix critical pair theorem (for term rewriting).     

Bisimulation from Open Maps

An abstract definition of bisimulation is presented. It makes possible a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets), and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a strengthening of the history-preserving bisimulation of Rabinovitch and Traktenbrot and van Glabeek and Goltz. A tie-up with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has “refinement” operators. The general approach yields a logic, generalising Hennessy–Milner logic, which is characteristic for the generalised notion of bisimulation.     

Building Interpreters with Rewriting Strategies

Programming language semantics based on pure rewrite rules suffers from the gap between the rewriting strategy implemented in rewriting engines and the intended evaluation strategy. This paper shows how programmable rewriting strategies can be used to implement interpreters for programming languages based on rewrite rules. The advantage of this approach is that reduction rules are first class entities that can be reused in different strategies, even in other kinds of program transformations such as optimizers. The approach is illustrated with several interpreters for the lambda calculus based on implicit and explicit (parallel) substitution, different strategies including normalization, eager evaluation, lazy evaluation, and lazy evaluation with updates. An extension with pattern matching and choice shows that such interpreters can easily be extended.     

Relating state-based and process-based concurrency through linear logic (full-version)

This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones.Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the well established state-transformation model inspired by Petri nets and multiset rewriting, and the prolific process-based models such as the π-calculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic and observe that, possibly modulo duality, they invariably target a small semantic fragment of linear logic that we call LV^obs.In the second part of the paper, we propose a new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of linear logic and specifically LV^obs. The resulting interpretation is extended with a majority of linear connectives into the language of ω-multisets. This interpretation drops the distinction between multiset elements and rewrite rules, and considerably enriches the expressive power of standard multiset rewriting with embedded rules, choice, replication, and more. Derivations are now primarily viewed as open objects, and are closed only to examine intermediate rewriting states. The resulting language can also be interpreted as a process algebra. For example, a simple translation maps process constructors of the asynchronous π-calculus to rewrite operators. The language of ω-multisets forms the basis for the security protocol specification language MSR 3. With relations to both multiset rewriting and process algebra, it supports specifications that are process-based, state-based, or of a mixed nature, with the potential of combining verification techniques from both worlds. Additionally, its logical underpinning makes it an ideal common ground for systematically comparing protocol specification languages.     

Proving termination of (conditional) rewrite systems

In this paper an important problem in the domain of term rewriting, the termination of (conditional) rewrite systems, is dealt with. We show that in many applications, well-founded orderings on terms which only make use of syntactic information of a rewrite systemR, do not suffice for proving termination ofR. Indeed sometimes semantic information is needed to orient a rewrite rule. Therefore we integrate a semantic interpretation of rewrite systems and terms into a well-founded ordering on terms: the notion ofsemantic ordering is the first main contribution of this paper. The use and usefulness of the semantic ordering in proving termination is illustrated by means of some realistic examples.Furthermore the concept of semantic information induces a novel approach for proving termination inconditional rewrite systems. The idea is to employ not only semantic information contained in the terms that are to be compared, but also extra (semantic) information contained in the premiss of the conditional equation in which the terms appear. This leads to our second contribution in the termination problem area: the notion ofcontextual ordering andcontextual semantic ordering. Thecontextual approach allows to prove termination of conditional rewrite systems where all classical partial orderings would fail.     

Probabilistic logic programming

Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming have restricted themselves to non-probabilistic semantic characterizations. In this paper, we take a few steps towards rectifying this situation. We define a logic programming language that is syntactically similar to the annotated logics of Blair et al., 1987 and Blair and Subrahmanian, 1988, 45–73) but in which the truth values are interpreted probabilistically. A probabilistic model theory and fixpoint theory is developed for such programs. This probabilistic model theory satisfies the requirements proposed by Fenstad (in “Studies in Inductive Logic and Probabilities” (R. C. Jeffrey, Ed.), Vol. 2, pp. 251–262, Univ. of California Press, Berkeley, 1980) for a function to be called probabilistic. The logical treatment of probabilities is complicated by two facts: first, that the connectives cannot be interpreted truth-functionally when truth values are regarded as probabilities; second, that negation-free definite-clause-like sentences can be inconsistent when interpreted probabilistically. We address these issues here and propose a formalism for probabilistic reasoning in logic programming. To our knowledge, this is the first probabilistic characterization of logic programming semantics.     

Exploring models for semantic category verification

Many artificial intelligence tasks, such as automated question answering, reasoning, or heterogeneous database integration, involve verification of a semantic category (e.g. “coffee” is a drink, “red” is a color, while “steak” is not a drink and “big” is not a color). In this research, we explore completely automated on-the-fly verification of a membership in any arbitrary category which has not been expected a priori. Our approach does not rely on any manually codified knowledge (such as WordNet or Wikipedia) but instead capitalizes on the diversity of topics and word usage on the World Wide Web, thus can be considered “knowledge-light” and complementary to the “knowledge-intensive” approaches. We have created a quantitative verification model and established (1) what specific variables are important and (2) what ranges and upper limits of accuracy are attainable. While our semantic verification algorithm is entirely self-contained (not involving any previously reported components that are beyond the scope of this paper), we have tested it empirically within our fact seeking engine on the well known TREC conference test questions. Due to our implementation of semantic verification, the answer accuracy has improved by up to 16% depending on the specific models and metrics used.     

Two Case Studies of Semantics Execution in Maude: CCS and LOTOS

We explore the features of rewriting logic and, in particular, of the rewriting logic language Maude as a logical and semantic framework for representing and executing inference systems. In order to illustrate the general ideas we consider two substantial case studies. In the first one, we represent both the semantics of Milner’s CCS and a modal logic for describing local capabilities of CCS processes. Although a rewriting logic representation of the CCS semantics is already known, it cannot be directly executed in the default interpreter of Maude. Moreover, it cannot be used to answer questions such as which are the successors of a process after performing an action, which is used to define the semantics of Hennessy-Milner modal logic. Basically, the problems are the existence of new variables in the righthand side of the rewrite rules and the nondeterministic application of the semantic rules, inherent to CCS. We show how these problems can be solved in a general, not CCS dependent way by controlling the rewriting process by means of reflection. This executable specification plus the reflective control of rewriting can be used to analyze CCS processes. The same techniques are also used to implement a symbolic semantics for LOTOS in our second case study. The good properties of Maude as a metalanguage allow us to implement a whole formal tool where LOTOS specifications without restrictions in their data types (given as ACT ONE specifications) can be executed. In summary, we present Maude as an executable semantic framework by providing easy-tool-building techniques for a language given its operational semantics.Research supported by CICYT projects Desarrollo Formal de Sistemas Distribuidos (TIC97-0669-C03-01) and Desarrollo Formal de Sistemas Basados en Agentes Móviles (TIC2000-0701-C02-01).     

自动文摘基集语句的提取与润色的数学模型

针对统计和理解相结合的自动文摘方法,提出了一种新的内容词、有效词和特征词的动态加权函数以及句子重要性的动态加权函数.鉴于基于统计的自动文摘结果常常出现语句间缺乏连贯性及信息冗余的问题,设计了句间语义距离测试函数,并通过大量实验确定语句间语义距离的上限和下限.上限用于控制语句间的逻辑联系,下限用于解决文摘结果信息冗余的问题.实验结果证明,该模型能有效地提取文章中的重点语句,且很好地解决了统计文摘语句不连冠的瓶颈问题.     

Lifting Infinite Normal Form Definitions From Term Rewriting to Term Graph Rewriting

nfinite normal forms are a way of giving semantics to non-terminating rewrite systems. The notion is a generalization of the Böhm tree in the lambda calculus. It was first introduced in [Ariola, Z. M. and S. Blom, Cyclic lambda calculi, in: Abadi and Ito [Abadi, M. and T. Ito, editors, “Theoretical Aspects of Computer Software,” Lecture Notes in Computer Science 1281, Springer Verlag, 1997], pp. 77–106] to provide semantics for a lambda calculus on terms with letrec. In that paper infinite normal forms were defined directly on the graph rewrite system. In [Blom, S., “Term Graph Rewriting - syntax and semantics,” Ph.D. thesis, Vrije Universiteit Amsterdam (2001)] the framework was improved by defining the infinite normal form of a term graph using the infinite normal form on terms. This approach of lifting the definition makes the non-confluence problems introduced into term graph rewriting by substitution rules much easier to deal with. In this paper, we give a simplified presentation of the latter approach.     

Countering the loss of extended vigilance in supervisory control using a fuzzy logic model

When an operator first detects unusual and/or infrequent or irregular signals in a system, the operator does not need to take any action, but must increase his/her level of attention and be alert for any more serious signals that may confirm a problem with the system. This is referred to as extended vigilance. The purpose of this study was to construct a fuzzy vigilance-measuring model for countering the loss of extended vigilance. The model extends two-valued logic (“Yes” or “No”) to multi-valued logic through fuzzy sets. Then a fuzzy logic alarm was developed by the model for combating the extended vigilance decrement. The first experiment compared the effect of the fuzzy measuring model with signal detection theory (SDT) and discussed the relationship between preliminary and extended vigilance for a simulated feed-water monitoring system. The results indicated that the sensitivity of the fuzzy vigilance-measuring model is better than index d′ and β, and that the preliminary vigilance significantly influences the extended vigilance. The second experiment verified the effect of the fuzzy logic alarm. The results indicated that the effect of the fuzzy logic alarm for combating the extended vigilance decrement is significant. When the preliminary vigilance is poor, an appropriate alarm will improve the extended vigilance. However, if the preliminary vigilance is very poor, the improvement of the extended vigilance will be limited.Relevance to industry: The extended vigilance is a new and important issue in human performance problems in industry, particularly in such areas as air-traffic control, industrial inspection and power plant monitor. The measuring model of vigilance could be applied to develop an alarm for promoting supervisory performance of human and human–machine detectors.