Reasoning about preferences in argumentation frameworks

The abstract nature of Dung's seminal theory of argumentation accounts for its widespread application as a general framework for various species of non-monotonic reasoning, and, more generally, reasoning in the presence of conflict. A Dung argumentation framework is instantiated by arguments and a binary conflict based attack relation, defined by some underlying logical theory. The justified arguments under different extensional semantics are then evaluated, and the claims of these arguments define the inferences of the underlying theory. To determine a unique set of justified arguments often requires a preference relation on arguments to determine the success of attacks between arguments. However, preference information is often itself defeasible, conflicting and so subject to argumentation. Hence, in this paper we extend Dung's theory to accommodate arguments that claim preferences between other arguments, thus incorporating meta-level argumentation based reasoning about preferences in the object level. We then define and study application of the full range of Dung's extensional semantics to the extended framework, and study special classes of the extended framework. The extended theory preserves the abstract nature of Dung's approach, thus aiming at a general framework for non-monotonic formalisms that accommodate defeasible reasoning about as well as with preference information. We illustrate by formalising argument based logic programming with defeasible priorities in the extended theory.     

Reasoning about actions with loops via Hoare logic

Plans with loops are more general and compact than classical sequential plans, and gaining increasing attentions in artificial intelligence (AI). While many existing approaches mainly focus on algorithmic issues, few work has been devoted to the semantic foundations on planning with loops. In this paper, we first develop a tailored action language AL K, together with two semantics for handling domains with non-deterministic actions and loops. Then we propose a sound and (relative) complete Hoare-style proof system for efficient plan generation and verification under 0-approximation semantics, which uses the so-called idea offline planning and on-line querying strategy in knowledge compilation, i.e., the agent could generate and store short proofs as many as possible in the spare time, and then perform quick query by constructing a long proof from the stored shorter proofs using compositional rule. We argue that both our semantics and proof system could serve as logical foundations for reasoning about actions with loops.     

Reasoning about UML/OCL class diagrams using constraint logic programming and formula

Model Driven Engineering promotes the use of models as the main artifacts in software and system development. Verification and validation of models are key activities to ensure the quality of the system under development. This paper presents a framework to reason about the satisfiability of class models described using the Unified Modeling Language (UML). The proposed framework allows us to identify possible design flaws as early as possible in the software development cycle. More specifically, we focus on UML Class Diagrams annotated with Object Constraint Language (OCL) invariants, which are considered to be the main artifacts in Object-Oriented analysis and design for representing the static structure of a system. We use the Constraint Logic programming (CLP) paradigm to reason about UML Class Diagrams modeling foundations. In particular, we use Formula as a model-finding and design space exploration tool. We also present an experimental Eclipse plug-in, which implements our UML model to Formula translation proposal following a Model Driven Architecture (MDA) approach. The proposed framework can be used to reason, validate, and verify UML Class Diagram software designs by checking correctness properties and generating model instances using the model exploration tool Formula.     

A new modal logic for reasoning about space: spatial propositional neighborhood logic

It is widely accepted that spatial reasoning plays a central role in artificial intelligence, for it has a wide variety of potential applications, e.g., in robotics, geographical information systems, and medical analysis and diagnosis. While spatial reasoning has been extensively studied at the algebraic level, modal logics for spatial reasoning have received less attention in the literature. In this paper we propose a new modal logic, called spatial propositional neighborhood logic (SpPNL for short) for spatial reasoning through directional relations. We study the expressive power of SpPNL, we show that it is able to express meaningful spatial statements, we prove a representation theorem for abstract spatial frames, and we devise a (non-terminating) sound and complete tableaux-based deduction system for it. Finally, we compare SpPNL with the well-known algebraic spatial reasoning system called rectangle algebra.      

Reasoning about probabilistic sequential programs in a probabilistic logic

We introduce a notion of strong monotonicity of probabilistic predicate transformers. This notion enables us to establish a normal form theorem for monotone probabilistic predicate transformers. Three other healthiness conditions, namely, conjunctivity, disjunctivity and continuity for probabilistic predicate transformers are also examined, and they are linked to strong monotonicity. A notion of probabilistic refinement index is proposed, and it provides us with a continuous strength spectrum of refinement relations which may be used to describe more flexible refinement between probabilistic programs. A notion of probabilistic correctness is introduced too. We give a probabilistic weakest-precondition, choice and game semantics to the contract language, and present a probabilistic generalization of the winning strategy theorem. Received: 16 April 2002 / 20 January 2003 RID="a" ID="a" This work was partly supported by the National Key Project for Fundamental Research of China (Grant No: 1998030905) and the National Foundation of Natural Sciences of China (Grant No: 60273003)     

Reasoning about ignorance and contradiction: many-valued logics versus epistemic logic

This paper tries to reinterpret three- and four-valued logics of partial ignorance and contradiction in the light of epistemic logic. First, we try to cast Kleene three-valued logic in the setting of a simplified form of epistemic logic. It is a two-tiered logic that embeds propositional logic into another propositional setting. The use of modalities enables Kleene truth values to be expressed at the syntactic level. Kleene logic is then a fragment of the simplified epistemic logic where modalities are in front of literals only. Kleene truth-tables can then be retrieved, while preserving tautologies of classical logic. Kleene logic connectives can be seen as set-valued extensions of Boolean logic ones, but the compositionality of Kleene logic leads to a lack of expressiveness and inferential power compared to the proposed epistemic logic. This methodology is then extended to Belnap four-valued logic, which is tailored to the handling of inconsistent information from various sources. A non-regular modal setting for reasoning about contradiction is obtained, where the adjunction law does not hold. It is a special case of a fragment of the monotonic modal logic EMN.     

Generalized quantifiers and modal logic

We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness both of modal systems and of systems in the quantifier tradition, complexity as well as syntactic characterizations of special semantic constraints. Throughout the paper several techniques current in the theory of generalized quantifiers are used to obtain results in modal logic, and conversely.This author was supported by the Foundation for Philosophical Research (SWON), which is subsidized by the Netherlands Organization for Scientific Research (NWO).     

Specifying coalgebras with modal logic

We propose to use modal logic as a logic for coalgebras and discuss it in view of the work done on coalgebras as a semantics of object-oriented programming. Two approaches are taken: First, standard concepts of modal logic are applied to coalgebras. For a certain kind of functor it is shown that the logic exactly captures the notion of bisimulation and a complete calculus is given. Examples of verifications of object properties are given. Second, we discuss the relationship of this approach with the coalgebraic logic of Moss (Coalgebraic logic, Ann Pure Appl. Logic 96 (1999) 277–317.).     

Reasoning about almost-certain convergence properties using Event-B

We propose an approach for proving that a system guarantees to establish a given property eventually with probability one. Using Event-B as our modelling language, our correctness reasoning is a combination of termination proofs (in terms of probabilistic convergence), deadlock-freedom and invariant techniques. We illustrate the approach by formalising some non-trivial algorithms, including the duelling cowboys, Herman’s probabilistic self-stabilisation and Rabin’s choice coordination. We extend the supporting Rodin Platform (Rodin) of Event-B to generate appropriate proof obligations for our reasoning, then subsequently (automatically/interactively) discharge the obligations using the built-in provers of Rodin.     

Reasoning about Action Systems using the B-Method

The action system formalism has been succesfully used when constructing parallel and distributed systems in a stepwise manner within the refinement calculus. Usually the derivation is carried out manually. In order to be able to produce more trustworthy software, some mechanical tool is needed. In this paper we show how action systems can be derived and refined within the B-Toolkit, which is a mechanical tool supporting a software development method, the B-Method. We describe how action systems are embedded in the B-Method. Furthermore, we show how a typical and nontrivial refinement rule, the superposition refinement rule, is formalized and applied on action systems within the B-Method. In addition to providing tool support for action system refinement we also extend the application area of the B-Method to cover parallel and distributed systems. A derivation towards a distributed load balancing algorithm is given as a case study.     

A modal logic internalizing normal proofs

In the proof-theoretic study of logic, the notion of normal proof has been understood and investigated as a metalogical property. Usually we formulate a system of logic, identify a class of proofs as normal proofs, and show that every proof in the system reduces to a corresponding normal proof. This paper develops a system of modal logic that is capable of expressing the notion of normal proof within the system itself, thereby making normal proofs an inherent property of the logic. Using a modality △ to express the existence of a normal proof, the system provides a means for both recognizing and manipulating its own normal proofs. We develop the system as a sequent calculus with the implication connective ⊃ and the modality △, and prove the cut elimination theorem. From the sequent calculus, we derive two equivalent natural deduction systems.     

From modal logic to terminal coalgebras

We define a modal logic whose models are coalgebras of a polynomial functor. Bisimilarity turns out to be the same as logical equivalence. Ideas and concepts of modal logic are directly applied to the theory of coalgebras: we give an axiomatization and define canonical coalgebras. That leads to a completeness result. Each canonical coalgebra proves to be terminal in a certain class of coalgebras. The approach also yields a functional characterization of the terminal coalgebra of all coalgebras with respect to a given polynomial functor.     

Reasoning about software using metrics and expert opinion

When comparing software programs on the basis of more than one metric a difficulty arises when the metrics are contradictory or if there are no standard acceptance thresholds. An appealing solution in such cases is to incorporate expert opinion to resolve the inconsistencies. A rigorous framework, however, is essential when fusing metrics and expert opinion in this decision-making process. Fortunately, the analytical hierarchy process (AHP) can be used to facilitate rigorous decision-making in this particular problem. In this work a combination of expert opinion and tool-collected measures are used to reason about software programs using AHP. The methodology employed can be adapted to other decision-making problems in software engineering when both metrics data and expert opinion are available, some of which are described. This paper is an extended version of Norita Ahmad and Phillip A. Laplante, “Employing Expert Opinion and Software Metrics for Reasoning About Software,” Third IEEE International Symposium on Dependable, Autonomic and Secure Computing (DASC 2007), September 2007, Columbia, Maryland, USA.     

Rewrite rule systems for modal propositional logic

This paper explains new results relating modal propositional logic and rewrite rule systems. More precisely, we give complete term rewriting systems for the modal propositional systems known as K, Q, T, and S5. These systems are presented as extensions of Hsiang's system for classical propositional calculus. We have checked local confluence with the rewrite rule system K.B. (cf. the Knuth-Bendix algorithm) developed by the Formel project at INRIA. We prove that these systems are noetherian, and then infer their confluence from Newman's lemma. Therefore each term rewriting system provides a new automated decision procedure and defines a canonical form for the corresponding logic. We also show how to characterize the canonical forms thus obtained.     

A modal logic for message passing processes

A first-order modal logic is given for describing properties of processes which may send and receive values or messages along communication ports. We give two methods for proving that a process enjoys such a property. The first is the construction, for each processP and formulaF, of acharacteristic formula P satF such thatP enjoys the propertyF if and only if the formulaP satF is logically equivalent to tt. The second is a sound and complete proof system whose judgements take the formB P: F, meaning: under the assumptionB the processP enjoys the propertyF.The notion ofsymbolic operational semantics plays a crucial role in the design of both the characteristic formulae and the proof system.This work was been supported by the SERC grant GR/H16537 and the ESPRIT BRA CONCUR II     

格值模态命题逻辑及其完备性

文中以满足第一及第二无限分配律的完备格为工具,建立了格值模态命题逻辑的语义理论,并指出这种语义是经典模态命题逻辑语义理论及[0,1]值模态命题逻辑语义理论的共同推广.给出了QMR0代数的定义,并分别以Boole代数及QMR0代数为背景构建了Boole型格值模态命题逻辑系统B及QMR0型格值模态命题逻辑系统QML*,并证明了系统B及系统QML*的完备性.