Results 11  20
of
49
Modal Logic: A Semantic Perspective
 ETHICS
, 1988
"... This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimul ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimulations) which underly it. We introduce the syntax and semantics of basic modal logic, discuss its expressivity at the level of models, examine its computational properties, and then consider what it can say at the level of frames. We then move beyond the basic modal language, examine the kinds of expressivity offered by a number of richer modal logics, and try to pin down what it is that makes them all ‘modal’. We conclude by discussing an example which brings many of the ideas we discuss into play: games.
Transformational Design of RealTime Systems Part I: From Requirements to Program Specifications
 Acta Informatica
, 1997
"... In the two parts of this article a transformational approach to the design of distributed realtime systems is presented. The starting point are global requirements formulated in a subset of Duration Calculus called implementables and the target are programs in an occam dialect PL. In the first ..."
Abstract

Cited by 13 (4 self)
 Add to MetaCart
In the two parts of this article a transformational approach to the design of distributed realtime systems is presented. The starting point are global requirements formulated in a subset of Duration Calculus called implementables and the target are programs in an occam dialect PL. In the first part we show how the level of program specifications represented by a language SL can be reached. SL combines regular expressions with ideas from action systems and with time conditions, and can express the distributed architecture of the implementation. While Duration Calculus is statebased, SL is eventbased, and the switch between these two worlds is a prominent step in the transformation from implementables to SL. Both parts of the transformational calculus rely on the mixed term techniques by which syntax pieces of two languages are mixed in a semantically coherent manner. In the first part of the article mixed terms between implementables and SL and in the second part of the article mixed terms between SL and PL are used. The approach is illustrated by the example of a computer controlled gas burner.
Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of NonClassical Logics I
 Studia Logica
, 1998
"... The main goal of this paper is to explain the link between the algebraic and the Kripkestyle models for certain classes of propositional logics. We start by presenting a Priestleytype duality for distributive lattices endowed with a general class of wellbehaved operators. We then show that fin ..."
Abstract

Cited by 12 (6 self)
 Add to MetaCart
The main goal of this paper is to explain the link between the algebraic and the Kripkestyle models for certain classes of propositional logics. We start by presenting a Priestleytype duality for distributive lattices endowed with a general class of wellbehaved operators. We then show that finitelygenerated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and nontopological Kripkestyle models for logics that are sound and complete with respect to varieties of distributive lattices with operators in the abovementioned classes. Introduction In the study of nonclassical propositional logics (and especially of modal logics) there are two main ways of defining interpretations or models. One possibility is to use algebras  usually lattices with operators  as models. Propositional variables are interpreted over elements of these algebraic models, an...
Axiomatic characterization of the AGM theory of belief revision in a temporal logic
 Artificial Intelligence
"... www.elsevier.com/locate/artint Since belief revision deals with the interaction of belief and information over time, branchingtime temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the nexttime temporal operator, contains ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
www.elsevier.com/locate/artint Since belief revision deals with the interaction of belief and information over time, branchingtime temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the nexttime temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatic characterization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiomatic characterization of the full set of AGM postulates.
A simple modal logic for belief revision
 and Knowledge, Rationality and Action
, 2005
"... We propose a modal logic based on three operators, representing intial beliefs, information and revised beliefs. Three simple axioms are used to provide a sound and complete axiomatization of the qualitative part of Bayes ’ rule. Some theorems of this logic are derived concerning the interaction bet ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
We propose a modal logic based on three operators, representing intial beliefs, information and revised beliefs. Three simple axioms are used to provide a sound and complete axiomatization of the qualitative part of Bayes ’ rule. Some theorems of this logic are derived concerning the interaction between current beliefs and future beliefs. Information flows and iterated revision are also discussed. 1
Belief revision in a temporal framework
 New Perspectives on Games and Interaction, volume 4 of Texts in Logic and Games
, 2009
"... The theory of belief revision deals with (rational) changes in beliefs in response to new information. In the literature a distinction has been drawn between belief revision and belief update (see [6]). The former deals with situations where the objective facts describing the world do not change (so ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
The theory of belief revision deals with (rational) changes in beliefs in response to new information. In the literature a distinction has been drawn between belief revision and belief update (see [6]). The former deals with situations where the objective facts describing the world do not change (so that only the beliefs of the
Possibilistic Reasoning  A Minisurvey and Uniform Semantics
 Artificial Intelligence
, 1996
"... In this paper, we survey some quantitative and qualitative approaches to uncertainty management based on possibility theory and present a logical framework to integrate them. The semantics of the logic is based on the Dempster's rule of conditioning for possibility theory. It is then shown that clas ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
In this paper, we survey some quantitative and qualitative approaches to uncertainty management based on possibility theory and present a logical framework to integrate them. The semantics of the logic is based on the Dempster's rule of conditioning for possibility theory. It is then shown that classical modal logic, conditional logic, possibilistic logic, quantitative modal logic and qualitative possibilistic logic are all sublogics of the present logical framework. In this way, we can formalize and generalize some wellknown results about possibilistic reasoning in a uniform semantics. Moreover, our uniform framework is applicable to nonmonotonic reasoning, approximate consequence relation formulation, and partial consistency handling. Key words: Nonclassical logics, possibility theory, conditional possibility, modal logic, conditional logic. 1 Introduction There are essentially two kinds of logical formalisms for reasoning about possibility and necessity. On the one hand, the qua...
Larger automata and less work for LTL model checking
 In Model Checking Software, 13th Int’l SPIN Workshop, volume 3925 of LNCS
, 2006
"... Abstract. Many different automata and algorithms have been investigated in the context of automatatheoretic LTL model checking. This article compares the behaviour of two variations on the widely used Büchi automaton, namely (i) a Büchi automaton where states are labelled with atomic propositions a ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Abstract. Many different automata and algorithms have been investigated in the context of automatatheoretic LTL model checking. This article compares the behaviour of two variations on the widely used Büchi automaton, namely (i) a Büchi automaton where states are labelled with atomic propositions and transitions are unlabelled, and (ii) a form of testing automaton that can only observe changes in state propositions and makes use of special livelock acceptance states. We describe how these variations can be generated from standard Büchi automata, and outline an SCCbased algorithm for verification with testing automata. The variations are compared to standard automata in experiments with both random and humangenerated Kripke structures and LTL X formulas, using SCCbased algorithms as well as a recent, improved version of the classic nested search algorithm. The results show that SCCbased algorithms outperform their nested search counterpart, but that the biggest improvements come from using the variant automata. Much work has been done on the generation of small automata, but small automata do not necessarily lead to small products when combined with the system being verified. We investigate the underlying factors for the superior performance of the new variations. 1
A syntactic approach to rationality in games with ordinal payoffs
 Logic and the Foundations of Game and Decision Theory, Texts in Logic and Games Series
, 2008
"... We consider strategicform games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another str ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We consider strategicform games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another strategy is better. We show that common belief of this weak notion of rationality characterizes the iterated deletion of pure strategies that are strictly dominated by pure strategies. The second axiom says that a player is irrational if she chooses a particular strategy while believing that a different strategy is at least as good and she considers it possible that this alternative strategy is actually better than the chosen one. We show that common knowledge of this stronger notion of rationality characterizes the restriction to pure strategies of the iterated deletion procedure introduced by Stalnaker (1994). Frame characterization results are also provided. 1
Development of Correct RealTime Systems by Refinement
, 1997
"... Contents I The Background 1 1 Instead of an Introduction: Formal Methods in Computing Science 3 1.1 How to get Systems Correct . . . . . . . . . . . . . . . . . . . . . 4 1.2 On the Use of Formal Methods . . . . . . . . . . . . . . . . . . . 4 1.3 Essentials of Formal Methods . . . . . . . . . . . ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Contents I The Background 1 1 Instead of an Introduction: Formal Methods in Computing Science 3 1.1 How to get Systems Correct . . . . . . . . . . . . . . . . . . . . . 4 1.2 On the Use of Formal Methods . . . . . . . . . . . . . . . . . . . 4 1.3 Essentials of Formal Methods . . . . . . . . . . . . . . . . . . . . 6 1.4 Some Classical Formal Approaches . . . . . . . . . . . . . . . . . 8 1.5 Formal Approaches to Realtime Restrictions . . . . . . . . . . . 10 1.6 The ProCoS Approach . . . . . . . . . . . . . . . . . . . . . . . . 13 1.7 The Aim of the Habilitationsschrift . . . . . . . . . . . . . . . . . 14 1.8 The Structure of the Habilitationsschrift . . . . . . . . . . . . . . 16 2 Modal Logic and the Duration Calculus 19 2.1 What is Modal Logic? . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 The Systems T, S4 and S5 . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Modal and Temporal Logic . . . . . . . . . . . . . . . . . . . .