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Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
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
A Logic for Reasoning about Time and Reliability
 Formal Aspects of Computing
, 1994
"... We present a logic for stating properties such as, "after a request for service there is at least a 98% probability that the service will be carried out within 2 seconds". The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabilities. Formulas are inter ..."
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Cited by 360 (1 self)
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We present a logic for stating properties such as, "after a request for service there is at least a 98% probability that the service will be carried out within 2 seconds". The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabilities. Formulas are interpreted over discrete time Markov chains. We give algorithms for checking that a given Markov chain satisfies a formula in the logic. The algorithms require a polynomial number of arithmetic operations, in size of both the formula and This research report is a revised and extended version of a paper that has appeared under the title "A Framework for Reasoning about Time and Reliability" in the Proceeding of the 10 th IEEE Realtime Systems Symposium, Santa Monica CA, December 1989. This work was partially supported by the Swedish Board for Technical Development (STU) as part of Esprit BRA Project SPEC, and by the Swedish Telecommunication Administration. the Markov chain. A simple example is inc...
Decision Procedures and Expressiveness in the Temporal Logic of Branching Time
, 1985
"... We consider the computation tree logic (CTL) proposed in (Set. Comput. Programming 2 ..."
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Cited by 190 (4 self)
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We consider the computation tree logic (CTL) proposed in (Set. Comput. Programming 2
Relevance logic and concurrent composition
 In Proceedings of Third Annual Symposium on Logic in Computer Science
, 1988
"... We show that the operation of relativising properties with respect to parallel environments often employed in obtaining compositionality in theories for concurrency corresponds to a notion of (contraction—free) relevant deduction. We propose to consider program logics in which this notion of deducti ..."
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We show that the operation of relativising properties with respect to parallel environments often employed in obtaining compositionality in theories for concurrency corresponds to a notion of (contraction—free) relevant deduction. We propose to consider program logics in which this notion of deduction is internalized by means of the corresponding implication. The idea is carried through for safety properties of a simple system of SCCStype synchronuous processes with an internal choice operator. We present two completeness results; first for a modal extension of positive propositional linear logic w.r.t. the equational class of algebras containing the safety testing quotient of our process system as its free member, and secondly for the free algebra itself.
Branching Time and Partial Order in Temporal Logics
 Time and Logic: A Computational Approach
, 1995
"... The aim of this paper is to present existing propositional temporal logics with branching and partially ordered time. These logics are used for specifying and proving properties of programs and systems. The branching time approach is useful e.g. for nondeterministic programs and can be applied ..."
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The aim of this paper is to present existing propositional temporal logics with branching and partially ordered time. These logics are used for specifying and proving properties of programs and systems. The branching time approach is useful e.g. for nondeterministic programs and can be applied also for concurrent programs. The partial order approach is especially useful for concurrent programs and allows one to study more subtle properties than those based on branching time. A survey of branching time logics, computation tree logics, partial order temporal logics and logics based on event structures is given. The following issues are concerned in this paper: the completeness of proof systems, the finite model property, decidability, model checking and expressiveness of the logics. 1 Introduction The aim of this paper is to present existing formal languages of propositional temporal logic with frames based on branching time structures or, more general, partial orders. Bran...
Propositional dynamic logic of flowcharts
 Infor. and Control
, 1985
"... Following a suggestion of Pratt, we consider propositional dynamic logic in which programs are nondeterministic finite automata o~¢er atomic programs and tests (i.e., flowcharts), rather than regular expressions. While the resulting version of PDL, call it APDL, is clearly equivalent in expressive p ..."
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Cited by 14 (2 self)
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Following a suggestion of Pratt, we consider propositional dynamic logic in which programs are nondeterministic finite automata o~¢er atomic programs and tests (i.e., flowcharts), rather than regular expressions. While the resulting version of PDL, call it APDL, is clearly equivalent in expressive power to PDL, it is also (in the worst case) exponentially more succinct. In particular, deciding its validity problem by reducing it to that of PDL leads to a double exponential time procedure, although PDL itself is decidable in exponential time. We present an elementary combined proof of the completeness of a simple axiom system for APDL and decidability of the validity problem in exponential time. The results are thus stronger than those for PDL, since PDL can be encoded in APDL with no additional cost, and the proofs simpler, since induction on the structure of programs is virtually eliminated. Our axiom system for APDL relates to the PDL system just as Floyd's proof method for partial correctness relates to Hoare's. © 1985 Academic Press, Inc. 1.
A logic of agent programs
 In Proc. of the National Conference on Artificial Intelligence (AAAI
, 2007
"... We present a sound and complete logic for reasoning about SimpleAPL programs. SimpleAPL is a fragment of the agent programming language 3APL designed for the implementation of cognitive agents with beliefs, goals and plans. Our logic is a variant of PDL, and allows the specification of safety and l ..."
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We present a sound and complete logic for reasoning about SimpleAPL programs. SimpleAPL is a fragment of the agent programming language 3APL designed for the implementation of cognitive agents with beliefs, goals and plans. Our logic is a variant of PDL, and allows the specification of safety and liveness properties of agent programs. We prove a correspondence between the operational semantics of SimpleAPL and the models of the logic for two example program execution strategies. We show how to translate agent programs written in SimpleAPL into expressions of the logic, and give an example in which we show how to verify correctness properties for a simple agent program.
Reasoning about agent deliberation
 In Proc. of the 11th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR’08
, 2008
"... We present a family of sound and complete logics for reasoning about deliberation strategies for SimpleAPL programs. SimpleAPL is a fragment of the agent programming language 3APL designed for the implementation of cognitive agents with beliefs, goals and plans. The logics are variants of PDL, and a ..."
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We present a family of sound and complete logics for reasoning about deliberation strategies for SimpleAPL programs. SimpleAPL is a fragment of the agent programming language 3APL designed for the implementation of cognitive agents with beliefs, goals and plans. The logics are variants of PDL, and allow us to prove safety and liveness properties of SimpleAPL agent programs under different deliberation strategies. We show how to axiomatize different deliberation strategies for SimpleAPL programs, and, for each strategy we consider, prove a correspondence between the operational semantics of SimpleAPL and the models of the corresponding logic. We illustrate the utility of our approach with an example in which we show how to verify correctness properties for a simple agent program under different deliberation strategies.
An Axiomatic Semantics of Concurrent Programming Languages
, 1984
"... this paper, I present a new compositional, truly axiomatic semantics for concurrent programming languages. It is based upon temporal logic, but employs five fundamental ideas beyond those found in most temporal logic methods: ..."
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Cited by 5 (3 self)
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this paper, I present a new compositional, truly axiomatic semantics for concurrent programming languages. It is based upon temporal logic, but employs five fundamental ideas beyond those found in most temporal logic methods: