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Dynamic Logic
 Handbook of Philosophical Logic
, 1984
"... ed to be true under the valuation u iff there exists an a 2 N such that the formula x = y is true under the valuation u[x=a], where u[x=a] agrees with u everywhere except x, on which it takes the value a. This definition involves a metalogical operation that produces u[x=a] from u for all possibl ..."
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Cited by 826 (7 self)
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ed to be true under the valuation u iff there exists an a 2 N such that the formula x = y is true under the valuation u[x=a], where u[x=a] agrees with u everywhere except x, on which it takes the value a. This definition involves a metalogical operation that produces u[x=a] from u for all possible values a 2 N. This operation becomes explicit in DL in the form of the program x := ?, called a nondeterministic or wildcard assignment. This is a rather unconventional program, since it is not effective; however, it is quite useful as a descriptive tool. A more conventional way to obtain a square root of y, if it exists, would be the program x := 0 ; while x < y do x := x + 1: (1) In DL, such programs are firstclass objects on a par with formulas, complete with a collection of operators for forming compound programs inductively from a basis of primitive programs. To discuss the effect of the execution of a program on the truth of a formula ', DL uses a modal construct <>', which
Coinductive Axiomatization of Recursive Type Equality and Subtyping
, 1998
"... e present new sound and complete axiomatizations of type equality and subtype inequality for a firstorder type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The mai ..."
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Cited by 66 (2 self)
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e present new sound and complete axiomatizations of type equality and subtype inequality for a firstorder type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The main novelty of the axiomatization is the fixpoint rule (or coinduction principle), which has the form A; P ` P A ` P (Fix) where P is either a type equality = 0 or type containment 0 and the proof of the premise must be contractive in a formal sense. In particular, a proof of A; P ` P using the assumption axiom is not contractive. The fixpoint rule embodies a finitary coinduction principle and thus allows us to capture a coinductive relation in the fundamentally inductive framework of inference systems. The new axiomatizations are more concise than previous axiomatizations, particularly so for type containment since no separate axiomatization of type equality is required, as in A...
Temporal Description Logics: A Survey
, 2008
"... We survey temporal description logics that are based on standard temporal logics such as LTL and CTL. In particular, we concentrate on the computational complexity of the satisfiability problem and algorithms for deciding it. ..."
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Cited by 28 (9 self)
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We survey temporal description logics that are based on standard temporal logics such as LTL and CTL. In particular, we concentrate on the computational complexity of the satisfiability problem and algorithms for deciding it.
Logicbased Knowledge Representation
 Artificial Intelligence Today, Recent Trends and Developments, number 1600 in Lecture Notes in Computer Science
, 1996
"... . After a short analysis of the requirements that a knowledge representation language must satisfy, we introduce Description Logics, Modal Logics, and Nonmonotonic Logics as formalisms for representing terminological knowledge, timedependent or subjective knowledge, and incomplete knowledge res ..."
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Cited by 28 (0 self)
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. After a short analysis of the requirements that a knowledge representation language must satisfy, we introduce Description Logics, Modal Logics, and Nonmonotonic Logics as formalisms for representing terminological knowledge, timedependent or subjective knowledge, and incomplete knowledge respectively. At the end of each section, we briefly comment on the connection to Logic Programming. 1 Introduction This section is concerned with the question under which conditions one may rightfully claim to have represented knowledge about an application domain, and not just stored data occurring in this domain. 1 In the early days of Artificial Intelligence and Knowledge Representation, there was a heated discussion on whether logic can at all be used as a formalism for Knowledge Representation (see e.g. [135, 91, 92]). One aspect of the requirements on knowledge representation formalisms that can be derived from the considerations in this section is very well satisfied by logical for...
Runtime monitoring of electronic contracts
 In ATVA’08, LNCS
, 2008
"... Abstract. Electronic interorganizational relationships are governed by contracts regulating their interaction. It is necessary to runtime monitor the contracts, as to guarantee their fulfillment. The present work shows how to obtain a runtime monitor for contracts written in CL, a formal specific ..."
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Cited by 14 (5 self)
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Abstract. Electronic interorganizational relationships are governed by contracts regulating their interaction. It is necessary to runtime monitor the contracts, as to guarantee their fulfillment. The present work shows how to obtain a runtime monitor for contracts written in CL, a formal specification language which allows to write conditional obligations, permissions and prohibitions over actions. The trace semantics of CL formalizes the notion of a trace fulfills a contract. We show how to obtain, for a given contract, an alternating Büchi automaton which accepts exactly the traces that fulfill the contract. This automaton is the basis for obtaining a finite state machine which acts as a runtime monitor for CL contracts. 1
A Complete Deductive System for the µCalculus
, 1995
"... The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper ..."
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Cited by 13 (0 self)
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The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper
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 ..."
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Cited by 12 (2 self)
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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.
CL: An Actionbased Logic for Reasoning about Contracts ⋆
"... Abstract. This paper presents a new version of the CL contract specification language. CL combines deontic logic with propositional dynamic logic but it applies the modalities exclusively over structured actions. CL features synchronous actions, conflict relation, and an action negation operation. T ..."
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Cited by 6 (3 self)
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Abstract. This paper presents a new version of the CL contract specification language. CL combines deontic logic with propositional dynamic logic but it applies the modalities exclusively over structured actions. CL features synchronous actions, conflict relation, and an action negation operation. The CL version that we present here is more expressive and has a cleaner semantics than its predecessor. We give a direct semantics for CL in terms of normative structures. We show that CL respects several desired properties from legal contracts and is decidable. We relate this semantics with a trace semantics of CL which we used for runtime monitoring contracts. 1