D. Kozen andJ. Tiuryn. Handbook of Theoretical Computer Science, pages790--840. Elsevier Science Publishers (NorthHolland) Amsterdam,1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....do people call them program logics And why do we give non mathematical names for them 22 The answers are quite simple. Program logics are modal logics used in software and hardware veri cation and speci cation for reasoning about programs. In 1980s program logics comprised dynamic logics [15, 18, 16], temporal logics [27, 9] and their extensions by means of xpoints. EPDL is the simplest dynamic logic; C is a very expressive extension of EPDL by xpoints and . Temporal logics are fragments of C with a single action variable next for discrete nexttime. A more recent addition to the ....

....10 100 states, since with large sets representation problem arises. We would like to give some recommendations on further reading on program logics. Some books and special chapter of handbooks can be recommended for those who are interested in the theory of program logics : rst [12] then [15, 16, 27, 18, 9] (in any order) There are also several books which discuss the pragmatics and applications of program logics. A comprehensive survey (from the implementation perspective) on automatic model checking techniques and applications is given in [6] The temporal logic approach to speci cation and to ....

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Kozen D., Tiuryn J. Logics of Programs. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, p.789-840.

....expressive than 2M, is as expressive as the Second order Logic of monadic Successors of M. Rabin (S(n)S Logic ) but still enjoys equal model checking power with CTL, C and 2M (in the same settings as above) 1 CTL and C vs. Second Order Logics The propositional Calculus of D. Kozen (C ) [10, 11] is a powerful propositional program logic with fixpoints. In particular, a very popular with model checking community state based temporal Computation Tree Logic (CTL) 7, 4, 5] is interpretable in C . It is almost a folklore that CTL is less expressive than C . Nevertheless, expressibility ....

Kozen D., Tiuryn J. Logics of Programs. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, 789-840.

....the title Program logics made easy And why do we give non mathematical names for them The answers are quite simple. Program logics are modal logics used in softand hardware verification and specification for reasoning about programs. In 1980 ies program logics comprised ffl dynamic logics [14, 16], ffl temporal logics [15, 17] and their extensions by means of fixpoints. A more recent addition to the family of program logics is logic of knowledge [18] The utility of this logic for this application is that it provides a language that formalizes constructs capturing notions that are used ....

....become more important as soon as model checking is applied to huge models with, say, 10 100 states, since large sets representation problem arises. 46 6. 3 Concluding remarks We would like to recommend some further reading on mathematical theory of program logics 26 : first [18] 14] 15] [16] [17] z in any order. For those who are interested in applications of program logics some reading is recommended below also. Temporal logic have been shown to provide a convenient framework for specifying and reasoning about properties of a broad class of systems which can be presented ....

Kozen D., Tiuryn J. Logics of Programs. Handbook of Theoretical Computer Science, v.B, Elsilver and The MIT Press, 1990, p.789-840.

....people call them Program logics And why do we give non mathematical names for them The answers are quite simple. Program logics are modal logics used in soft19 ware and hardware verification and specification for reasoning about programs. In 1980 ies program logics comprised ffl dynamic logics [15, 18, 16], ffl temporal logics [29, 9] and their extensions by means of fixpoints. EPDL is the simplest dynamic logic, C is a very expressive extension of EPDL by fixpoints and . Temporal logics are fragments of C with a single action variable next for discrete next time. A more recent addition to the ....

....say, 10 100 states, since large sets representation problem arises. I would like to give some recommendations on further reading on program logics. Some books and special chapter of handbooks can be recommended for those who is interested in theory of program logics 11 : first [12] then [15, 16, 29, 18, 9] (in any order) There are also several books which discuss pragmatics and applications of program logics. A comprehensive survey (from implementation perspective) on automatic model checking techniques and applications is given in [6] Temporal logic approach to specification and to manual ....

[Article contains additional citation context not shown here]

Kozen D., Tiuryn J. Logics of Programs. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, p.789-840.

....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 1 SOEPDL vs. Propositional Program Logics The propositional Calculus of D. Kozen (C) [6, 7] is a powerful propositional program logic with fixpoints. In particular, a very popular with model checking community state based temporal Computation Tree Logic (CTL) 4, 2, 3] is expressible in C. We give a new proof that CTL is less expressive than C: Proposition 1 1. No CTL formula can ....

Kozen D., Tiuryn J. Logics of Programs. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, 789-840.

....2 and seq 2 j= T (X s ) 5. seq j= T (j Uw ) iff either seq i j= T j for every finite i jseqj, or seq j j= T for some finite j jseqj and seq i j= T j for every finite i j. The Second Order Propositional Dynamic Logic (SOPDL) 20] is an extension of Propositional Dynamic Logic (PDL) [23, 24, 29, 25, 26] with quantifiers over propositional variables. The syntax of SOPDL is constructed from the same alphabets B and P as above and from an additional finite alphabet A of action variables. The syntax consists of (non deterministic monadic program (Ianov) schemata S and (logical) formulae FSO . A ....

Kozen D., Tiuryn J. Logics of Programs. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, p.789-840.

....provability as a modal operator corresponds to multi conclusion proof systems. Single operators t : in LP are not normal modalities since they do not satisfy the property t : P Q) t : P t : Q) This makes LP essentially different from polymodal logics, e.g. the dynamic logic of programs ([54]) where the modality is upgraded by some additional features. Rather in 12 SERGEI N. ARTEMOV the Logic of Proofs the modality is decomposed into a family of proof polynomials (see x9) x6. Standard provability interpretation of LP. In x6 and x8 by Delta 1 and Sigma 1 we mean the corresponding ....

D. Kozen and J. Tiuryn, Logic of programs, Handbook of theoretical computer science. Volume B, Formal models and semantics (J. van Leeuwen, editor), Elsevier, 1990, pp. 789--840.

....enumerative and symbolic search methods. While we argue in favor of the linear time framework, we also we argue that LTL is not expressive enough, and discuss what would be the ultimate temporal specification language. We assume familiarity with the syntax and semantics of temporal logic [30,53,94]. 2 CTL 2.1 Expressiveness It is important to understand that expressiveness is not merely a theoretical issue; expressiveness is also a usability issue. Verification engineers find CTL unintuitive. The linear framework is simply more natural for verification engineers, who tend to think ....

D. Kozen and L. Tiuryn. Logics of programs. Handbook of Theoretical Computer Science, pages 789--840, 1990.

....language like Pascal, C, C , or Java. So another paradigm would be better in this case than the functional one. It should be a paradigm which captures imperative style and fixed points simultaneously. This is a Program Logics paradigm in general, and the formalism of the propositional Calculus [3] in particular. But this formalism is in the most comprehensive form that relies upon transfinite induction and some basic modal logics: it is not easy to make the Calculus easy for undergraduates In this case another hint is an incremental approach to the introduction of the Calculus in finite ....

D. Kozen and J. Tiuryn, Logics of Programs. Handbook of Theoretical Computer Science, v.B, Elsevier and The MIT Press, 1990, p.789-840.

....verification [KV98] In each case we show that CTL does not dominate LTL computationally. In the concluding section of the paper we discuss the implication of these results on the linearvs. branching time discussion. We assume familiarity with the syntax and semantics of temporal logic [Eme90, KT90, Sti92] 2 Modular Model Checking Model checking is known to suffer from the socalled state explosion problem. In a concurrent setting, the system under consideration is typically the parallel composition of many modules. As a result, the size of the state space of the system is the prod ....

D. Kozen and L. Tiuryn. Logics of programs. Handbook of Theoretical Computer Science, pages 789--840, 1990.

....their values from other inferences. The data flow connects inputs and outputs of inferences to the roles. Finally, the control of a PSM describes the ordering of execution of the inferences. In this paper we will use a procedural representation for this, based on quantified dynamic logic [Har84, Koz90] Therefore, the building blocks of our language are formulas and programs. Atomic formulas are formulas over the contents of roles, and complex formulas can be built in the usual manner. There are two types of primitive programs: i) a formula followed by a test operator , and (ii) programs ....

....and operational descriptions of the method has to be established. One has to ensure, that given the assumptions the operational descriptions describes a way to achieve the functionality. As the description of the operational specification requires a logic over states, we use dynamic logic ( Har84, Koz90] to formalize this obligation: j= 8I : precondition(I) assumptions) hpsm op iTrue j= 8I9O : precondition(I) assumptions) psm op ]psm dec (I ; O) The first obligation ensures the termination of the program and the second obligation ensures that the desired functionality is provided. ....

D. Kozen. Handbook of Theoretical Computer Science. Elsevier Science Publ., B. V., Amsterdam, 1990.

....) K4) #a## = # (K5) X. X ) # X. X ) K6) # X. X ) # (K7) X. X ) X. X ) The propositional calculus is an interesting logic because it is both expressive and manageable. It subsumes most propositional temporal logics and propositional modal logics of programs [2, 10, 16]. Over Kripke structures which are binary trees the logic is as expressive as S2S [12] monadic second order logic of two successors [14] On the other hand the validity A NOTE ON THE COMPLETENESS OF KOZEN S AXIOMATISATION 351 problem for calculus formulas is EXPTIME complete [3] This makes it ....

.... tableaux are up till now essentially the only method of model construction for the calculus [17] see [9] for a slightly di#erent approach) In particular this means that filtration based methods, so successful for proving completeness of various systems of modal logics and logics of programs [5, 10], do not adapt easily to the calculus. This problem exhibits itself in the fact that calculus does not have the collapsed model property. This property says that given a formula and its model, we can collapse the model by unifying states satisfying the same subformulas of the given formula, and ....

D. Kozen and J. Tiuryn, Logics of programs, Handbook of theoretical computer science (J. Leeuven, editor), vol. B, Elsevier, 1990, pp. 789--840.

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D. Kozen andJ. Tiuryn. Handbook of Theoretical Computer Science, pages790--840. Elsevier Science Publishers (NorthHolland) Amsterdam,1990.

No context found.

D. Kozen and J. Tiuryn, Logic of programs, Handbook of theoretical computer science. Volume B, Formal models and semantics (J. van Leeuwen, editor), Elsevier, 1990, pp. 789--840.

No context found.

Kozen, D. and Tiuryn, J. Logics of programs. Handbook of Theoretical Computer Science. Elsevier and The MIT Press, 1990, 789--840.

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