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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 1008 (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
Reasoning about Infinite Computations
 Information and Computation
, 1994
"... We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all ..."
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Cited by 316 (59 self)
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We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all have the same expressive power and that their decision problems are all PSPACEcomplete. We also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem. 1 Introduction For many years, logics of programs have been tools for reasoning about the input/output behavior of programs. When dealing with concurrent or nonterminating processes (like operating systems) there is, however, a need to reason about infinite computations. Thus, instead of considering the first and last states of finite computations, we need to consider the infinite sequences of states that the program goes through...
Complexity Results for TwoWay and MultiPebble Automata and their Logics
 Theoretical Computer Science
, 1996
"... : Twoway and multipebble automata are considered (the latter appropriately restricted to accept only regular languages), and enriched with additional features, such as nondeterminism and concurrency. We investigate the succinctness of such machines, and the extent to which this succinctness carrie ..."
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: Twoway and multipebble automata are considered (the latter appropriately restricted to accept only regular languages), and enriched with additional features, such as nondeterminism and concurrency. We investigate the succinctness of such machines, and the extent to which this succinctness carries over to make the reasoning problem in propositional dynamic logic (PDL) more difficult. The two main results establish that each additional pebble provides inherent exponential power on both fronts. 1 Introduction 1.1 Background This paper continues our work in [H], [DH], [HRV], seeking exponential (or higher) discrepancies in the succinctness of finite automata when augmented with various additional mechanisms. It is wellknown, for example, that NFAs are exponentially more succinct than DFAs, in the following upper and lower bound senses (see [RS], [MF]): (i) Any NFA can be simulated by a DFA with at most an exponential growth in size; (ii) There is a family of regular sets, L n , for ...
CL: An Actionbased Logic for Reasoning about Contracts
, 2009
"... 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 ver ..."
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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.
A Dynamic Deontic Logic for Complex Contracts
, 2011
"... We present a dynamic deontic logic for specifying and reasoning about complex contracts. The concepts that our contract logic CL captures are drawn from legal contracts, as we consider that these are more general and expressive than what is usually found in computer science (like in software contra ..."
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Cited by 5 (3 self)
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We present a dynamic deontic logic for specifying and reasoning about complex contracts. The concepts that our contract logic CL captures are drawn from legal contracts, as we consider that these are more general and expressive than what is usually found in computer science (like in software contracts, web services specifications, or communication protocols). CL is intended to be used in specifying complex contracts found in computer science. This influences many of the design decisions behind CL. We adopt an oughttodo approach to deontic logic and apply the deontic modalities exclusively over complex actions. On top, we add the modalities of dynamic logic so to be able to reason about what happens after an action is performed. CL can reason about regular synchronous actions capturing the notion of actions done at the same time. CL incorporates the notions of contrarytoduty and contrarytoprohibition by attaching to the deontic modalities explicitly a reparation which is to be enforced in case of violations. Results of decidability and tree model property are given as well as specific properties for the modalities.
A New Proof of Exponential Decidability for the Propositional µCalculus with Program Converse
 In III International Conference on Theoretical Aspects of Computer Science, Novi Sad, Yugoslavia
, 2000
"... The propositional Calculus (C) is a powerful propositional program logic with fixpoints. C decidability with exponential upper bound was sketched for the first time in 1988 by E. A. Emerson and Ch. S. Jutla on base of automatatheoretic technique, while a complete proof was published in 1999 on ..."
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The propositional Calculus (C) is a powerful propositional program logic with fixpoints. C decidability with exponential upper bound was sketched for the first time in 1988 by E. A. Emerson and Ch. S. Jutla on base of automatatheoretic technique, while a complete proof was published in 1999 only. Meanwhile M. Vardi sketched in 1998 an automatatheoretic proof of exponential decidability for the propositional Calculus with program converse (C \Gamma ). We believe that alternative, independent and automatafree proofs of exponential decidabilities for C and for C \Gamma are important for validation of these upper bounds and due to a complexity of automatatheoretic proofs. Previously the author published in 1997 a proof of exponential upper bound for C which exploited a socalled Program Schemata Technique (PST) for decidability of propositional program logics. This time an extended PST is applied to C \Gamma and yields exponential upper bound too. Subject classification: 03B25  Decidability of theories and sets of sentences, 03B70  Logic in Computer Science, 68Q60  Specification and verification. This work is supported by Creative Research Initiatives of the Korean Ministry of Science and Technology y While on leave from A.P. Ershov Institute of Informatics Systems of Siberian Division of Russian Academy of Science, Novosibirsk, Russia 1 Key words: program schemata, program logics, fixpoints, second order quantifiers. 1
Abstract ANNALS OF PURE AND APPLIED LOGIC
"... A new process logic is defined, called computation paths logic (CPL). which treats lbnn~~la~ and programs essentially alike. CPL is a pathwlse extension of PDL. following the basic ptocess logic of Harel. Kozen and Parikh. and is close in spirit to the logic R of Hare1 and Peleg. It enjoys most of ..."
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A new process logic is defined, called computation paths logic (CPL). which treats lbnn~~la~ and programs essentially alike. CPL is a pathwlse extension of PDL. following the basic ptocess logic of Harel. Kozen and Parikh. and is close in spirit to the logic R of Hare1 and Peleg. It enjoys most of the advantages of previous process logics. yet is decidable in elementary tlmc. We also ofrcr extensions for modeling asynchronouaisynchronous concurrency and infinite computanons. All extensions are also shown to be decidable in elementary time.:g 1999 Elsevicr Scicncr
Games with SecondOrder Quantifiers which Decide Propositional Program Logics
, 2001
"... The paper demonstrates how secondorder quantification and finite games can be exploited for deciding complicated propositional program logics like the propositional Calculus with converse (C \Gamma ). This approach yields a new proof that C \Gamma is in EXPT IME. ..."
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The paper demonstrates how secondorder quantification and finite games can be exploited for deciding complicated propositional program logics like the propositional Calculus with converse (C \Gamma ). This approach yields a new proof that C \Gamma is in EXPT IME.