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Dynamic Linear Time Temporal Logic
 IN ANNALS OF PURE AND APPLIED LOGIC
, 1997
"... A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S ..."
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Cited by 42 (3 self)
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A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S1S, the monadic secondorder theory of !sequences. In fact a sublogic of DLTL which corresponds to propositional dynamic logic with a linear time semantics is already as expressive as S1S. We pin down in an obvious manner the sublogic of DLTL which correponds to the first order fragment of S1S. We show that DLTL has an exponential time decision procedure. We also obtain an axiomatization of DLTL. Finally, we point to some natural extensions of the approach presented here for bringing together propositional dynamic and temporal logics in a linear time setting.
Process Logic: Expressiveness, Decidability, Completeness
, 1982
"... this paper have natural algebraic and topological interpretations: Let L be the Boolean algebra of formulas of PL modulo the PL axioms of Section 4, and let rim= {nXlXe Z}, fL=/fXlXe m } ..."
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Cited by 40 (1 self)
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this paper have natural algebraic and topological interpretations: Let L be the Boolean algebra of formulas of PL modulo the PL axioms of Section 4, and let rim= {nXlXe Z}, fL=/fXlXe m }
Dynamic Algebras as a wellbehaved fragment of Relation Algebras
 In Algebraic Logic and Universal Algebra in Computer Science, LNCS 425
, 1990
"... The varieties RA of relation algebras and DA of dynamic algebras are similar with regard to definitional capacity, admitting essentially the same equational definitions of converse and star. They differ with regard to completeness and decidability. The RA definitions that are incomplete with respect ..."
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Cited by 33 (5 self)
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The varieties RA of relation algebras and DA of dynamic algebras are similar with regard to definitional capacity, admitting essentially the same equational definitions of converse and star. They differ with regard to completeness and decidability. The RA definitions that are incomplete with respect to representable relation algebras, when expressed in their DA form are complete with respect to representable dynamic algebras. Moreover, whereas the theory of RA is undecidable, that of DA is decidable in exponential time. These results follow from representability of the free intensional dynamic algebras. Dept. of Computer Science, Stanford, CA 94305. This paper is based on a talk given at the conference Algebra and Computer Science, Ames, Iowa, June 24, 1988. It will appear in the proceedings of that conference, to be published by SpringerVerlag in the Lecture Notes in Computer Science series. This work was supported by the National Science Foundation under grant number CCR8814921 ...
Reasoning about Action and Change  A Dynamic Logic Approach
 Journal of Logic, Language, and Information
, 1996
"... this paper, we pursue a monotonic approach to the frame problem and concentrate on the combinatorial problem and the overcommitment problem. We will propose a solution within the framework of propositional dynamic logic (PDL)the modal logic of actions and of computer programs (see Pratt, 1976, 19 ..."
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Cited by 24 (0 self)
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this paper, we pursue a monotonic approach to the frame problem and concentrate on the combinatorial problem and the overcommitment problem. We will propose a solution within the framework of propositional dynamic logic (PDL)the modal logic of actions and of computer programs (see Pratt, 1976, 1980; Segerberg 1980; Harel, 1984). It is based on the idea of associating an operator [ff] with each action ff, the brackets being reminiscient of the box operator 2 of ordinary modal logic (see Hughes & Cresswell, 1984). The reading of a formula [ff]A is "after every terminating (halting) execution of ff, A is true." PDL provides a powerful language for describing compound actions such as sequential composition of actions ff and fi, written ff; fi, (nondeterministic) choice between ff and fi, written ff + fi, and (nondeterministic) iteration of ff, written ff
On induction vs. *continuity
 Proc. Workshop on Logics of Programs 1981, SpringVerlag Lect. Notes in Comput
, 1981
"... Abstract. In this paper we study the relative expressibility of the infinitary *continuity condition (*cant) X ~ V n x and the equational but weaker induction axiom Ond) X ^ [a*](X =[alX) [a*]X in Propositional Dynamic Logic. We show: (1) under ind only, there is a firstorder sentence ..."
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Cited by 20 (10 self)
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Abstract. In this paper we study the relative expressibility of the infinitary *continuity condition (*cant) <a*>X ~ V n <an>x and the equational but weaker induction axiom Ond) X ^ [a*](X =[alX) [a*]X in Propositional Dynamic Logic. We show: (1) under ind only, there is a firstorder sentence distinguishing separable dynamic algebras from standard Kripke models; whereas (2) under the stronger axiom *cant, the class of separable dynamic algebras and the class of standard Kripke models are indistinguishable by any sentence of infinitary firstorder logic. I.
Reasoning about Dynamic Policies
 Proceedings FoSSaCS7, Springer Lecture Notes in Computer Science 2987
, 2004
"... Abstract. People often need to reason about policy changes before they are adopted. For example, suppose a website manager knows that users want to enter her site without going through the welcome page. To decide whether or not to permit this, the wise manager will consider the consequences of modif ..."
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Cited by 18 (0 self)
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Abstract. People often need to reason about policy changes before they are adopted. For example, suppose a website manager knows that users want to enter her site without going through the welcome page. To decide whether or not to permit this, the wise manager will consider the consequences of modifying the policies (e.g., would this allow users to bypass advertisements and legal notices?). Similiarly, people often need to compare policy sets. For example, consider a person who wants to buy health insurance. Before choosing a provider, the customer will want to compare the different policies. In other words, the customer wants to reason about the effect of choosing one policy set over another. We introduce a logic, based on propositional dynamic logic, in which these tasks can be done. We give a sound and complete axiomatization for our logic, and also show that it is decidable. More precisely, the satisfiability problem is decidable in nondeterministic exponential time. 1
Dynamic Algebras: Examples, Constructions, Applications
 Studia Logica
, 1991
"... Dynamic algebras combine the classes of Boolean (B 0 0) and regular (R [ ; ) algebras into a single finitely axiomatized variety (B R 3) resembling an Rmodule with "scalar" multiplication 3. The basic result is that is reflexive transitive closure, contrary to the intuition that this con ..."
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Cited by 17 (1 self)
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Dynamic algebras combine the classes of Boolean (B 0 0) and regular (R [ ; ) algebras into a single finitely axiomatized variety (B R 3) resembling an Rmodule with "scalar" multiplication 3. The basic result is that is reflexive transitive closure, contrary to the intuition that this concept should require quantifiers for its definition. Using this result we give several examples of dynamic algebras arising naturally in connection with additive functions, binary relations, state trajectories, languages, and flowcharts. The main result is that free dynamic algebras are residually finite (i.e. factor as a subdirect product of finite dynamic algebras), important because finite separable dynamic algebras are isomorphic to Kripke structures. Applications include a new completeness proof for the Segerberg axiomatization of propositional dynamic logic, and yet another notion of regular algebra. Key words: Dynamic algebra, logic, program verification, regular algebra. This paper or...
Ascribing Beliefs to Resource Bounded Agents
, 2002
"... Logical approaches to reasoning about agents often rely on idealisations about belief ascription and logical omniscience which make it difficult to apply the results obtained to real agents. In this paper, we show how to ascribe beliefs and an ability to reason in an arbitrary decidable logic to an ..."
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Cited by 16 (7 self)
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Logical approaches to reasoning about agents often rely on idealisations about belief ascription and logical omniscience which make it difficult to apply the results obtained to real agents. In this paper, we show how to ascribe beliefs and an ability to reason in an arbitrary decidable logic to an agent in a computationally grounded way. We characterise those cases in which the assumption that an agent is logically omniscient in a given logic is `harmless' in the sense that it does not lead to making incorrect predictions about the agent, and show that such an assumption is not harmless when our predictions have a temporal dimension: `now the agent believes p', and the agent requires time to derive the consequences of its beliefs. We present a family of logics for reasoning about the beliefs of an agent which is a perfect reasoner in an arbitrary decidable logic L but only derives the consequences of its beliefs after some delay #. We investigate two members of this family in detail, L# in which all the consequences are derived at the next tick of the clock, and L # # in which the agent adds at most one new belief to its set of beliefs at every tick of the clock, and show that these are sound, complete and decidable.
Action emulation
 CWI and ILLC, Amsterdam & Department of Economics
, 2004
"... Abstract. The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multiagent models with update action models [3], now in widespread use (see [10] for a textbook treatment). There is a natural exten ..."
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Cited by 14 (6 self)
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Abstract. The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multiagent models with update action models [3], now in widespread use (see [10] for a textbook treatment). There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models gives the same result (modulo bisimulation). But the converse turns out to be false: update models may have the same update effects without being bisimilar. We propose action emulation as a notion of structural equivalence more appropriate for action models, and generalizing standard bisimulation. It is proved that action emulation provides a full characterization of update effect, provided we confine attention to ‘smooth ’ action models. We also give a recipe for turning any action model into a smooth one with the same update effect. Together, this yields a simplification procedure for action models, and it gives designers of multiagent systems a useful tool for comparing different ways of representing a particular communicative action. 1.