Cut-free sequent systems for temporal logic

Currently known sequent systems for temporal logics such as linear time temporal logic and computation tree logic either rely on a cut rule, an invariant rule, or an infinitary rule. The first and second violate the subformula property and the third has infinitely many premises. We present finitary cut-free invariant-free weakening-free and contraction-free sequent systems for both logics mentioned. In the case of linear time all rules are invertible. The systems are based on annotating fixpoint formulas with a history, an approach which has also been used in game-theoretic characterisations of these logics.     

Modeling and testing object-oriented distributed systems with linear-time temporal logic

We present a framework for constructing formal models of object-oriented distributed systems and a property language to express behavioral constraints in such models. Most of the existing models have their origin in specific mathematical notations and/or concepts. In contrast, we have developed our model such that it accounts for a large set of phenomena associated with industrial implementations of object-oriented distributed systems. The model that we propose, while closer to industrial concerns and practice, still has the powerful features of formal approaches. It also offers the possibility to automatically check at service run-time that the final service implementation has not violated and is not violating properties expressed at the abstraction level of our model. In our model, which relies on event-based behavioral abstraction, we use linear-time temporal logic as the underlying formalism for the specification of properties. We introduce two novel operators which are especially useful for object-oriented systems and which provide a number of advantages over the well-known temporal logic operators. A recent decision of one of our industrial partners to adopt our proposal into one of their development platforms can be seen as a strong evidence of the relevance of our work and as a promising step towards a better understanding between the academic formal methods community and industry. Copyright © 2001 John Wiley & Sons, Ltd.     

Completeness of a combination of neighbourhood logic and temporal logic

This paper presents a completeness result, with respect to a possible world semantics, for a combination of a first-order temporal logic and neighbourhood logic. This logic was considered by Qiu and Zhou (1998, Proceedings of the PROCOMET 98, pp 444–461) to define semantics of a real-time OCCAM-like programming language.Received June 1999Accepted in revised form September 2003 by M. R. Hansen and C. B. Jones     

Probabilistic Belief Logic and Its Probabilistic Aumann Semantics

In this paper, we present a logic system for probabilistic belief named PBL,which expands the language of belief logic by introducing probabilistic belief. Furthermore, we give the probabilistic Aumann semantics of PBL. We also list some valid properties of belief and probabilistic belief, which form the deduction system of PBL. Finally, we prove the soundness and completeness of these properties with respect to probabilistic Aumann semantics.     

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.     

Sequent calculi and decidability for intuitionistic hybrid logic

In this paper we study the proof theory of the first constructive version of hybrid logic called Intuitionistic Hybrid Logic (IHL) in order to prove its decidability. In this perspective we propose a sequent-style natural deduction system and then the first sequent calculus for this logic. We prove its main properties like soundness, completeness and also the cut-elimination property. Finally we provide, from our calculus, the first decision procedure for IHL and then prove its decidability.     

A temporal programming model with atomic blocks based on projection temporal logic

Atomic blocks, a high-level language construct that allows programmers to explicitly specify the atomicity of operations without worrying about the implementations, are a promising approach that simplifies concurrent programming. On the other hand, temporal logic is a successful model in logic programming and concurrency verification, but none of existing temporal programming models supports concurrent programming with atomic blocks yet. In this paper, we propose a temporal programming model （αPTL） which extends the projection temporal logic （PTL） to support concurrent programming with atomic blocks. The novel construct that formulates atomic execution of code blocks, which we call atomic interval formulas, is always interpreted over two consecutive states, with the internal states of the block being abstracted away. We show that the framing mechanism in projection temporal logic also works in the new model, which consequently supports our development of an executive language. The language supports concurrency by introducing a loose interleaving semantics which tracks only the mutual exclusion between atomic blocks. We demonstrate the usage of αPTL by modeling and verifying both the fine-grained and coarse-grained concurrency.     

A temporal programming model with atomic blocks based on projection temporal logic

Atomic blocks, a high-level language construct that allows programmers to explicitly specify the atomicity of operations without worrying about the implementations, are a promising approach that simplifies concurrent programming. On the other hand, temporal logic is a successful model in logic programming and concurrency verification, but none of existing temporal programming models supports concurrent programming with atomic blocks yet. In this paper, we propose a temporal programming model (αPTL) which extends the projection temporal logic (PTL) to support concurrent programming with atomic blocks. The novel construct that formulates atomic execution of code blocks, which we call atomic interval formulas, is always interpreted over two consecutive states, with the internal states of the block being abstracted away. We show that the framing mechanism in projection temporal logic also works in the new model, which consequently supports our development of an executive language. The language supports concurrency by introducing a loose interleaving semantics which tracks only the mutual exclusion between atomic blocks. We demonstrate the usage of αPTL by modeling and verifying both the fine-grained and coarse-grained concurrency.     

Formalization of UML state machines using temporal logic

The main purpose of this paper is to approach the use of formal methods in computing. In more specific terms, we use a temporal logic to formalize the most fundamental aspects of the semantics of UML state machines. We pay special attention to the dynamic aspects of the different operations associated with states and transitions, as well as the behaviour of transitions related with composite states. This, to the best of our knowledge, has not been done heretofore using temporal logic.Our formalization is based on a temporal logic that combines points, intervals, and dates. Moreover this new temporal logic is built over an innovative and simple topological semantics, which simplifies the metatheory development.     

从活性顺序图到时态逻辑的转化方法

为了将活性顺序图用于模型检测,方便描述系统的场景需求,提出了一种将活性顺序图转换成时态逻辑的转化方法.分析活性顺序图语言并且定义一种基于路径的语义,用活性顺序图表述系统的场景需求.根据提出的语义,给出了一个将场景需求显式转化为时态逻辑的一般方法,针对并发消息较多的系统扩展和优化此方法,以得到更简短的时态逻辑公式.通过实例说明活性顺序图到线性时态逻辑的转化过程.     

Common knowledge: Relating anti-founded situation semantics to modal logic neighbourhood semantics

Two approaches for defining common knowledge coexist in the literature: the infinite iteration definition and the circular or fixed point one. In particular, an original modelization of the fixed point definition was proposed by Barwise (1989) in the context of a non-well-founded set theory and the infinite iteration approach has been technically analyzed within multi-modal epistemic logic using neighbourhood semantics by Lismont (1993). This paper exhibits a relation between these two ways of modelling common knowledge which seem at first quite different.A first version of this paper was written while the author was an assistant at the Universite Catholique de Louvain. It was part of a doctoral thesis presented in June 1992.     

行为时态逻辑TLA定理系统证明及公平性研究

行为时态逻辑TLA(temporal logic of actions)能够在一种语言中同时表达模型程序与逻辑规则,是目前模型检测技术中一个较新的研究方向.为了理解行为时态逻辑与传统时态逻辑之间的理论联系,研究了时态逻辑的语义和定理系统,并根据行为时态逻辑TLA的自身特征指出了TLA中的行为属于时态逻辑T4系统.在此基础上严格的证明了TIA的定理系统及TLA中强公平性蕴涵弱公平性的重要性质,讨论了强公平性与弱公平性等价的条件.最后以实例说明了如何确定动作的强弱公平性,进而建立系统的TLA模型.     

Vectorial languages and linear temporal logic

Determining for a given deterministic complete automaton the sequence of visited states while reading a given word is the core of important problems with automata-based solutions, such as approximate string matching. The main difficulty is to do this computation efficiently. Considering words as vectors and working on them using vectorial operations allows to solve the problem faster than using local operations.

In this paper, we show first that the set of vectorial operations needed by an algorithm representing a given automaton depends on the language accepted by the automaton. We give precise characterizations for star-free, solvable and regular languages using vectorial algorithms. We also study classes of languages associated with restricted sets of vectorial operations and relate them with languages defined by fragments of linear temporal logic.

Finally, we consider the converse problem of constructing an automaton from a given vectorial algorithm. As a byproduct, we show that the satisfiability problem for some extensions of LTL characterizing solvable and regular languages is PSPACE-complete.     

Eigenvariables, bracketing and the decidability of positive minimal predicate logic

We give a new proof of a theorem of Mints that the positive fragment of minimal predicate logic is decidable. The idea of the proof is to replace the eigenvariable condition of sequent calculus by an appropriate scoping mechanism. The algorithm given by this proof seems to be more practical than that given by the original proof. A naive implementation is given at the end of the paper. Another contribution is to show that this result extends to a large class of theories, including simple type theory (higher-order logic) and second-order propositional logic. We obtain this way a new proof of the decidability of the inhabitation problem for positive types in system F.     

The Structure and Semantics of an Object-Oriented Logic Programming Language: SCKE

The development of the object-oriented paradigm has suffered from the lack of any generally accepted formal foundations for its semantic definition.To address this issue,we propose the development of the logic-based semantics of the object-oriented paradigm.By combining the logic-with the object-oriented paradigm of computing first,this paper discusses formally the semantics of a quite purely object-oriented logic paradigm in terms of proof theory,model theory and fixpoint theory from the viewpoint of logic.The operational and declarative semantics is given.And then the correspondence between soundness and completeness has been discussed formally.     

Dynamic event-triggered prescribed performance control for nonlinear systems with signal temporal logic

This article is concerned with the problem of dynamic event-triggered prescribed performance control for nonlinear systems under signal temporal logic tasks. By utilizing the method of prescribed performance control, the constrained plant can be transformed into an unconstrained one, and a dynamic event-triggered feedback control law is generated for the transformed system to ensure that the signal temporal logic specification is satisfied. A dynamic event-triggered mechanism is designed to guarantee the event-triggered stability, safety and complex specification. Besides, Zeno phenomenon is definitely avoided. Compared with the continuous-time feedback controller, the event-triggered controller has proven to be effective in reducing sensing, communication and computation costs. Finally, two simulations are given to illustrate the effectiveness of theoretical results.     

Axioms and models of linear logic

Girard's recent system of linear logic is presented in a way that avoids the two-level structure of formulae and sequents, and that minimises the number of primitive function symbols. A deduction theorem is proved concerning the classical implication as embedded in linear logic. The Hilbert-style axiomatisation is proved to be equivalent to the sequent formalism. The axiomatisation leads to a complete class of algebraic models. Various models are exhibited. On the meta-level we use Dijkstra's method of explicit equational proofs.     

An alternative approach to the semantics of disjunctive logic programs and deductive databases

In this paper, we study a new semantics of logic programming and deductive databases. Thepossible model semantics is introduced as a declarative semantics of disjunctive logic programs. The possible model semantics is an alternative theoretical framework to the classical minimal model semantics and provides a flexible inference mechanism for inferring negation in disjunctive logic programs. We also present a proof procedure for the possible model semantics and show that the possible model semantics has an advantage from the computational complexity point of view.This is a revised and extended version of the paper [36] which was presented at the Tenth International Conference on Logic Programming, Budapest, 21–25 June 1993.     

The red and black semantics: a fuzzy language

The complexity of abstract art languages create new semantics in art. This model tries to implement its conceptual language within creating a new virtual environment. The gap between art and technology has been approached with a fuzzy logic engine which uses a red and black semantic codification. The examples include the application of this metalanguage to a virtual artwork experimentation.