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We present a generalization of the temporal propositional logic of linear time which is useful for stating and proving properties of the generic execution sequence of a parallel program or a non-deterministic ... The models are tree models of arbitrary size similar to those used in branching time temporal logic. ... Note that sets of rst category can still be dense, for example, the set of all rational numbers is dense but is of rst category. ...doi:10.1006/inco.1996.0010 fatcat:2y3mgi5s6vbxrb4jzznozzwjku
It is shown that these specifications in temporal formalization can be executed, leading to a general al- gorithm for executing non-monotonic reasoning processes. ... Summary: “A propositional temporal logic is briefly introduced and its use for specification of reactive systems is motivated and illustrated. ...
Our proof system consists of three parts: a general part elaborating the properties of temporal logic, a domain part giving an axiomatic description of the data domain, and a program part giving an axiomatic ... We present a proof system in which properties of such programs, expressed as temporal formulas, can be proved formally. ...
A topological characterization of safety and liveness is given. Every property is shown to be the intersection of a safety property and a liveness property. ... A formal definition for liveness properties is proposed. ... Acknowledgment We wish to thank A. Demers, D. Gries, M. Krentel and E. Mallison for comments on an early draft of this paper. Comments from G. ...doi:10.1016/0020-0190(85)90056-0 fatcat:sgj2umqwnvdalknd2ewytirewi
In a general setting, the author shows that if an extension of the modal logic K is Kripke-complete and derives a formula with a particular property, then the Craig property for the logic implies the explicit ... As an application, we give semantics of modal proofs (a.k.a., programs) in categories of augmented simplicial sets and of topological spaces, and prove a completeness result in the style of Friedman: if ...
A property y is inevitable for a program p iff each execution of p necessarily passes through a state satisfying y. Total correctness and termination are examples of inevitable properties. ... Model checking is an effective and simple method for verifying that a concurrent program satisfies a temporal logic formula. ...
Lecture Notes in Computer Science
Clarke et al. (2004) have shown a similar result for general topologies and indexed LTL\X, provided processes cannot choose the directions for sending or receiving the token. ... We unify and substantially extend these results by systematically exploring fragments of indexed CTL * \X with respect to general topologies. ... We thank Roderick Bloem for detailed comments on numerous drafts and Krishnendu Chatterjee for important comments regarding the structure of the paper. ...doi:10.1007/978-3-642-54013-4_15 fatcat:yuw6mzutdvbl7kip7dvbsqou7y
Clarke et al. (2004) have shown a similar result for general topologies and indexed LTLX, provided processes cannot choose the directions for sending or receiving the token. ... We unify and substantially extend these results by systematically exploring fragments of indexed CTL^∗X with respect to general topologies. ... We thank Roderick Bloem for detailed comments on numerous drafts and Krishnendu Chatterjee for important comments regarding the structure of the paper. ...arXiv:1311.4425v3 fatcat:24ol5br6izc2rgky2fgurwjyoy
The high-profile and safety-critical nature of the application areas has fostered a large and growing body of work on formal methods for hybrid systems: mathematical logics, computational models and methods ... This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems. ... ACKNOWLEDGMENT The authors' view of hybrid systems and logics for reasoning about them has benefited from fruitful conversations and exchanges with many people; in particular, they would like to thank ...doi:10.1109/5.871305 fatcat:vsxl3q7h6rfcvbtxy4mmfnc7oi
We conclude with a brief discussion of how timesets fit into a general framework for proving properties of programs.” ... It involves the use of the temporal operator 01, where 0 A means that A is true for all times during the program execution. ...
We provide a Hilbert-style axiomatization for the proposed STSL PC and prove the soundness and completeness by the spatio-temporal extension of maximal consistent set and canonical model. ... In this paper, we present a spatio-temporal specification language, STSL PC, by combining Signal Temporal Logic (STL) with a spatial logic S4 u, to characterize spatio-temporal dynamic behaviors of cyber-physical ... Acknowledgments We would like to thank the anonymous reviewers for their valuable comments and suggestions, which helped improve the quality of this paper. ...doi:10.1186/s13677-020-00209-3 fatcat:7furkjr4nzdvllolt3ta33znha
Lecture Notes in Computer Science
I explore the history of, and lessons learned from, eighteen years of assertional methods for specifying and verifying concurrent programs. ... I then propose a Utopian future in which mathematics prevails. ... We can generalize ordinary temporal logic to include actions by defining [[A]], for any action A, to be true of a sequence iff it is true of the first pair of states: [[A]](s 0 , s 1 , . . . ) ∆ = A(s ...doi:10.1007/3-540-58043-3_23 fatcat:yfizmu2dorhklaj6t2dqsx6pkq
Lecture Notes in Computer Science
Ivy supports deductive verification using automated provers, model checking, automated testing, manual theorem proving and generation of executable code. ... This paper surveys the work to date on Ivy, a language and a tool for the formal specification and verification of distributed systems. ... However, a new technique  integrated into Ivy shows that on the contrary, the formalism of first-order logic provides a unique opportunity for proving liveness and temporal properties. ...doi:10.1007/978-3-319-99725-4_4 fatcat:hkqiqefpgra6jahbnk6pugvibu
Formal analysis of NOC communication will be very advantageous since it allows proving some theorems or interesting qualitative/quantitative properties on the communication behavior where simulation/emulation ... A NOC includes many applications that can execute concurrently. This situation may show some undesirable behaviors such as deadlock, livelock, starvation, etc. ... The properties are specified in linear temporal logic (LTL). ...doi:10.3991/ijes.v6i4.9416 fatcat:7fljmcayfvdgpd7v3d4vt7lkvu
Dynamic Formal Epistemology
Furthermore, as we are sometimes interested in multiple layers of conceptual structure, representing several layers of properties by allowing for several topologies in one system often proves fruitful. ... The topological space X of the IFS interprets spatial properties, while the function f determines the temporal behavior of the system. ...doi:10.1007/978-94-007-0074-1_5 fatcat:xh3ktk35bfdqdp6gf7qh3hv52y
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