1. Temporal Logic - Wikipedia, The Free Encyclopedia In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in http://en.wikipedia.org/wiki/Temporal_logic

Temporal logic From Wikipedia, the free encyclopedia Jump to: navigation search In logic , the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time . It is sometimes also used to refer to tense logic , a particular modal logic -based system of temporal logic introduced by Arthur Prior in the . Subsequently it has been developed further by computer scientists , notably Amir Pnueli , and logicians Temporal logic was first studied in depth by Aristotle , whose writings are filled with a crude form of first-order temporal modal binary logic. Any logic which uses the existential quantifier or the universal quantifier is said to be a first-order logic . Any logic which views time as a sequence of states is a temporal logic, and any logic which uses only two truth values is a binary logic Consider the statement: "I am hungry." Though its meaning is constant in time, the truth value of the statement can vary in time. Sometimes the statement is true, and sometimes the statement is false, but the statement is never true and false simultaneously. In a temporal logic, statements can have a truth value which can vary in time. Contrast this with an atemporal logic, which can only handle statements whose truth value is constant in time. In a temporal logic we can then express statements like "I am always hungry", "I will

2. Temporal Logic (Stanford Encyclopedia Of Philosophy) The term temporal logic has been broadly used to cover all approaches to the representation of temporal information within a logical framework, http://plato.stanford.edu/entries/logic-temporal/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free Temporal Logic First published Mon Nov 29, 1999; substantive revision Thu Dec 11, 2003 The term Temporal Logic has been broadly used to cover all approaches to the representation of temporal information within a logical framework, and also more narrowly to refer specifically to the modal-logic type of approach introduced around 1960 by Arthur Prior under the name of Tense Logic and subsequently developed further by logicians and computer scientists. Applications of Temporal Logic include its use as a formalism for clarifying philosophical issues about time, as a framework within which to define the semantics of temporal expressions in natural language, as a language for encoding temporal knowledge in artificial intelligence, and as a tool for handling the temporal aspects of the execution of computer programs. 1. Modal-logic approaches to temporal logic 2. Predicate-logic approaches to temporal logic 3. Philosophical issues 4. Applications ... Related Entries 1. Modal-logic approaches to temporal logic 1.1 Tense Logic

3. Foundations Of Temporal Logic - The WWW-site For Prior-studies Foundations of temporal logic The WWW-site for Prior-studies. http://www.kommunikation.aau.dk/prior/index2.htm

4. TLA - The Temporal Logic Of Actions TLA (the temporal logic of Actions) is a logic for specifying and reasoning about concurrent and reactive systems. It is the basis for TLA+, http://research.microsoft.com/users/lamport/tla/tla.html

TLA - The Temporal Logic of Actions Last modified 9 February 2004 The TLA+ book is available here The TLA+ tools are available here What is TLA? TLA (the Temporal Logic of Actions) is a logic for specifying and reasoning about concurrent and reactive systems. It is the basis for TLA+, a complete specification language. This Web page will be updated to reflect new work on TLA. I hope that all work on TLA and TLA tools will be accessible from here. If you want to be notified of changes to this page, or if you want your work to be represented here, please send e-mail to Leslie Lamport About TLA and TLA+ Introduction to TLA Leslie Lamport 16 December 1994 A short (7-page) introduction to what TLA formulas mean. It should allow you to understand TLA specifications. A Summary of TLA+ This is a 7-page "cheat sheet" that briefly describes all the constructs and built-in operators of TLA+ and the operators defined in the common standard modules, and that lists the user-definable operator symbols and the ascii representations of symbols. Postscript (300K) Compressed Postscript (170K) PDF (120K) PODC 2000 Tutorial Handout This is the handout from the TLA+ tutorial at PODC 2000. It will be meaningful only to people who attended the tutorial.

5. Temporal Logic Case Study A case study applying temporal logic to specify the operation of a bank of identical elevators servicing a number of floors in a building. http://www.sei.cmu.edu/publications/documents/89.reports/89.tr.024.html

Home Contact Us Site Map Search ... Acronyms Temporal Logic Case Study Wood, W. Technical Report CMU/SEI-89-TR-024 PDF File PostScript File This report is a case study applying temporal logic to specify the operation of a bank of identical elevators servicing a number of floors in a building. The goal of the study was to understand the application of temporal logic in a problem domain that is appropriate for the method, and to determine some of the strengths and weaknesses of temporal logic in this domain. The case study uses a finite state machine language to build a model of the system specification, and verifies that the temporal logic specifications are consistent using this model. The specification aspires to be complete, consistent, and unambiguous. Privacy Statement

6. Interval Temporal Logic A flexible notation for both propositional and firstorder reasoning about periods of time found in descriptions of hardware and software systems. http://www.cse.dmu.ac.uk/~cau/itlhomepage/

Interval Temporal Logic Antonio Cau Ben Moszkowski and Hussein Zedan Software Technology Research Laboratory January 15, 2008 Pdf version of the ITL home page ITL-course: A not so short introduction to ITL Abstract Interval Temporal Logic (ITL) is a flexible notation for both propositional and first-order reasoning about periods of time found in descriptions of hardware and software systems. Unlike most temporal logics, ITL can handle both sequential and parallel composition and offers powerful and extensible specification and proof techniques for reasoning about properties involving safety, liveness and projected time . Timing constraints are expressible and furthermore most imperative programming constructs can be viewed as formulas in a slightly modified version of ITL . Tempura provides an executable framework for developing and experimenting with suitable ITL specifications. In addition, ITL and its mature executable subset Tempura have been extensively used to specify the properties of real-time systems where the primitive circuits can directly be represented by a set of simple temporal formulae. In addition, various researchers have applied Tempura

7. Temporal Logic Definition of temporal logic, possibly with links to more information and implementations. http://www.nist.gov/dads/HTML/temporllogic.html

temporal logic (definition) Definition: A logic with a notion of time included. The formulas can express facts about past, present, and future states. The formulas are interpreted over Kripke structures, which can model computation; hence temporal logic is very useful in formal verification Author: SKS Implementation The SMV model checker. Go to the Dictionary of Algorithms and Data Structures home page. If you have suggestions, corrections, or comments, please get in touch with Paul E. Black Entry modified 17 December 2004. HTML page formatted Mon Sep 11 09:46:08 2006. Cite this as: Sandeep Kumar Shukla, "temporal logic", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology . 17 December 2004. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/temporllogic.html

8. Diagnosing Java Code: Assertions And Temporal Logic In Java Programming Although traditional assertions can increase the amount of checking that can be done over Java code, there are many checks you just can t perform with them. http://www.ibm.com/developerworks/java/library/j-diag0723.html

var emailAbstract = "Although traditional assertions can increase the amount of checking that can be done over Java code, there are many checks you just can't perform with them. One way to fill this gap is with temporal logic, a formalism used to describe how a program state will change over time. In this article, Eric Allen discusses assertions, introduces temporal logic, and describes a tool for processing temporal logic assertions in your programs."; Country/region select All of dW AIX and UNIX IBM Systems Information Mgmt Lotus Rational Tivoli WebSphere Architecture Autonomic computing Grid computing Java technology Linux Open source Power Architecture Web development XML dW forums alphaWorks All of IBM Home Products My IBM developerWorks ... Rate this page Related links Java technology technical library developerWorks Java technology Diagnosing Java code: Assertions and temporal logic in Java programming Introduce temporal logic to assertions to supplement testing Document options Document options requiring JavaScript are not displayed Discuss Rate this page Help us improve this content Level: Introductory Eric Allen eallen@cs.rice.edu

9. BRICS Lecture Series, Abstracts, 1997 A survey of the field by Jan Chomicki and David Toman. From the 1997 BRICS Lecture Series. http://www.brics.dk/LS/97/Abs/BRICS-LS-97-Abs/

BRICS Lecture Series, Abstracts, 1997 March 24, 1999 This document is also available as PostScript DVI Text References LS-97-1 PostScript PDF DVI Jan Chomicki and David Toman. Temporal Logic in Information Systems November 1997. viii+42 pp. Full version to appear in: Logics for Database and Information Systems, Chomicki and Saake (eds.), Kluwer Academic Publishers, 1998. Abstract: Temporal logic is obtained by adding temporal connectives to a logic language. Explicit references to time are hidden inside the temporal connectives. Different variants of temporal logic use different sets of such connectives. In this chapter, we survey the fundamental varieties of temporal logic and describe their applications in information systems. Several features of temporal logic make it especially attractive as a query and integrity constraint language for temporal databases. First, because the references to time are hidden, queries and integrity constraints are formulated in an abstract, representation-independent way. Second, temporal logic is amenable to efficient implementation. Temporal logic queries can be translated to an algebraic language. Temporal logic constraints can be efficiently enforced using auxiliary stored information. More general languages, with explicit references to time, do not share these properties. Recent research has proposed various implementation techniques to make temporal logic practically useful in database applications. Also, the relationships between different varieties of temporal logic and between temporal logic and other temporal languages have been clarified. We report on these developments and outline some of the remaining open research problems.

10. Modal And Temporal Logic - Course Details - Computing - Imperial College London Use of temporal logics LTL and CTL in the model checker NuSMV. Logics of knowledge and belief. Logics of action and duty, dynamic logic. http://www.doc.ic.ac.uk/teaching/coursedetails/499

Skip over navigation Quick Navigation Imperial home page A-Z of Departments Courses Research Alumni Faculty of Engineering Faculty of Life Sciences Faculty of Medicine Faculty of Physical Sciences Business School Spectrum (restricted to College users) People finder Help Note: Your browser does not support javascript or you have javascript turned off. Although this will not affect your accessibility to the content of this site, some of the advanced navigation features may not be available to you. Home Teaching Course Details Modal and Temporal Logic Note: Some of the graphical elements of this site are only visible to browsers that support accepted web standards . The content of this site is, however, accessible to any browser or Internet device. Modal and Temporal Logic Lecturers: Ian Hodkinson homepage Marek Sergot homepage For course notes click on the lecturers homepages. AIMS To develop skills in the use of modal and temporal logics for specification, knowledge representation and practical reasoning in artificial intelligence and software engineering. LEARNING OUTCOMES Knowledge and understanding Students should have assimilated the distinctive characteristics of modalities.

11. Linear Temporal Logic This contribution contains a shallow embedding of Linear temporal logic (LTL) based on a coinductive representation of program executions. http://coq.inria.fr/contribs/LTL.html

Linear Temporal Logic This contribution contains a shallow embedding of Linear Temporal Logic (LTL) based on a co-inductive representation of program executions. Temporal operators are implemented as inductive (respectively co-inductive) types when they are least (respectively greatest) fixpoints. Several general lemmas, that correspond to LTL rules, are proved. Download (archive compatible with Coq V8.1) Author: Solange Coupet-Grimal (Laboratoire d'Informatique Fondamentale de Marseille (LIF, UMR 6166).) Date: July 2002 Keywords: temporal logic, infinite transition systems, co-induction. The README file of the contribution: This page was automatically generated from this description file

12. Interval Temporal Logic Interval temporal logic (ITL) is an important class of temporal logic which was initally devised by Ben Moskowski in the 1980 s. http://www.cs.kent.ac.uk/people/staff/hb5/interval.html

Interval Temporal Logic Howard Bowman and Simon Thompson Interval Temporal Logic (ITL) is an important class of temporal logic which was initally devised by Ben Moskowski in the 1980's. Standard temporal logics (see e.g. this page ) are defined over infinite state models, for example, the models for Manna and Pnueli Linear Time Temporal Logic are infinite state sequences. However, in interval temporal logic the model theory is restricted to finite state sequences, called intervals (although, supporting infinite state sequences is currently being investigated). There are a number of reasons for being interested in such logics. One reason is that interval temporal logic lends itself to execution. This is apparent from Moskowski's initial work. In addition, a number of interesting and powerful operators arise naturally from ITL. In fact, it is straightforward to derive operators very like the constructs of imperative programming (e.g. assignment, conditionals, iteration etc). This then yields the possibility that abstract specifications and concrete implementations can be realised in the same notation, with refinement mappings between. An additional aspect of interval temporal logic is that it provides a very simple real-time model in which one unit of time is past when moving from state to state. Consequently, timings can be obtained by measuring interval lengths.

13. Existential Graphs And Tense Logic It should be noted that this thought is rather similar to ideas involved in the modern treatment of parallel systems with temporal logic based on branching http://www.hum.aau.dk/~poe/ARTIKLER/tense_graphs.html

Existential Graphs and Tense Logic by Department of Communication Aalborg University Langagervej 8 Denmark e-mail: poe@hum.auc.dk Tel: + 45 98 15 85 22 Fax: +45 98 15 94 34 Abstract. In this paper it is argued that the founder of modern tense logic, A.N. Prior was very much inspired by the logic and philosophy of C.S. Peirce. It is also demonstrated how the most important tense logical systems of Prior, K t , K c , and K b , can be reformulated in terms of the existential graphs invented by Peirce. In the 1950s and 1960s A. N. Prior succeeded in re-establishing a logic of time and tenses. It is obvious that the study of Peirce's philosophy meant a great deal to Prior and in his brief presentation of the history of the modern tense logic, to be found in the appendix to Prior's first great tense logical work "Time and Modality" [1957], elaborations of the importance of Peirce for the logic of time makes up about one fourth of the work. On the basis of his studies of Peirce's philosophy Prior even proposed a specific Peircean system of logic [Prior 1967, p.132]. This system he evidently found very attractive. There are many indications that Peirce, as one of the earliest modern philosophers, realized that tenses could, and even should, be reflected in our logic. He formulated his position in the following way:

14. Winter School, ISI Calcutta, January, 1997. Over the past two decades, temporal logic has become a very basic tool for specifying properties of reactive systems. For finitestate systems, http://www.cmi.ac.in/~madhavan/papers/isical97.html

Madhavan Mukund Tutorial talk, Winter School on Logic and Computer Science, Indian Statistical Institute, Calcutta, January 1997. Abstract Available as gzipped dvi (35 KB) , gzipped Postscript (79 KB) and PDF Back to Madhavan Mukund's home page

15. Alur/Henzinger/Kupferman: Alternating-time Temporal Logic temporal logic comes in two varieties lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system http://www.eecs.berkeley.edu/~tah/Publications/alternating-time_temporal_logic.h

Alternating-time Temporal Logic Rajeev Alur, Thomas A. Henzinger , and Orna Kupferman Temporal logic comes in two varieties: linear-time temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branching-time temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general variety of temporal logic: alternating-time temporal logic offers selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves. While linear-time and branching-time logics are natural specification languages for closed systems, alternating-time logics are natural specification languages for open systems. For example, by preceding the temporal operator "eventually" with a selective path quantifier, we can specify that in the game between the system and the environment, the system has a strategy to reach a certain state. The problems of receptiveness, realizability, and controllability can be formulated as model-checking problems for alternating-time formulas. Depending on whether or not we admit arbitrary nesting of selective path quantifiers and temporal operators, we obtain the two alternating-time temporal logics ATL and ATL*. ATL and ATL* are interpreted over concurrent game structures Journal of the ACM 49:672-713, 2002. Preliminary versions appeared in the

16. Temporal Logic This lecture gives a basic account of temporal logic from the viewpoint of computer science. Motivated by the specification of reactive and concurrent http://lat.inf.tu-dresden.de/teaching/ss2006/tl/

Temporal Logic Carsten Lutz Course Description This lecture gives a basic account of temporal logic from the viewpoint of computer science. Motivated by the specification of reactive and concurrent systems, we introduce both linear and branching-time temporal logics. We discuss the expressive power of such logics, relating them to one another, to first and second order logic, and to automata theory. We consider the two reasoning tasks model checking and satisfiability checking, and perform a detailed investigation of the computational complexity of these tasks. Prerequesites: basics of complexity theory will be helpful Organization Starting from June 12, the lecture will take place every Monday DS4 (13:00-14:00) in GRU 350 and every Thursday DS5 (14:50-16:20) in GRU 358 Lecture Material A script of the lecture is available. Credits / Examinations Computational logic students can earn 3 credits by attending this lecture. The lecture can be used for the modules SV and TCSL. In order to get the credits, CL students have to pass an oral examination at the end of the term. Literature The following literature is relevant for the lecture: E. Allen Emerson: Temporal and Modal Logic. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Elsevier, 1990.

17. Temporal Logic In Information Systems Jan Chomicki , David Toman , Michael H. Böhlen, Querying ATSQL databases with temporal logic, ACM Transactions on Database Systems (TODS), v.26 n.2, http://portal.acm.org/citation.cfm?id=294138

18. Temporal Logic As a basis for describing the genetic algorithm we will use a combination of classical firstorder logic, temporal logic 116 , and probabilistic logic http://lipas.uwasa.fi/cs/publications/2NWGA/node285.html

Next: Probabilistic Logic Up: Temporal Probabilistic Logic Previous: Temporal Probabilistic Logic Temporal Logic As a basis for describing the genetic algorithm we will use a combination of classical first-order logic, temporal logic [ , and probabilistic logic [ As far as temporal logic is concerned, our logic is based on temporal intervals, typically denoted I . Intervals may be used in expressions in various ways, using the following operators (table Given an interval I we have the following two operations on intervals. In order to reason within our logic we need to define some basic operators, in addition to the standard first-order logic with its boolean operators (disjunction), (conjunction), (negation), (implication) and (equivalence). We also have the first order operators (existence), and (universality). Following Manna and Pnueli [ , the temporal operators in table are sufficient for our purposes. Table: operators. p and q are general propositions. for intervals. Note that some of these operators are `weak' versions: wait-for is a weak version of the until operator which allows for the possibility that q never occurs and, then

19. Using Temporal Logic To Specify Properties Fortunately, SPIN does include a general propertychecking mechanism If we can state our property in a particular formal temporal logic, then SPIN will http://cnx.org/content/m12317/latest/

Contact Us Report a Bug Connexions Home ... Help You are here: Home Content » Using Temporal Logic to Specify Properties Content Actions Print (PDF) Save to del.icio.us (what's this?) Related material Similar content Concurrent Programming and Verification: Outline Model Checking Concurrent Programs Intro to Logic More » Collections using this content Model Checking Concurrent Programs Using Temporal Logic to Specify Properties Module by: Ian Barland John Greiner Moshe Vardi Note: Your browser doesn't currently support MathML. If you are using Microsoft Internet Explorer 6 or above, please install the required MathPlayer plugin . Firefox and other Mozilla browsers will display math without plugins, though they require an additional mathematics fonts package . Any browser can view the math in the Print (PDF) version So far, we've seen some of the built-in checks performed by SPIN: assertions, deadlock, non-progress, and one notion of fairness. But what about other properties we'd like to check for? We might be interested in properties which the implementors of our particular tool weren't interested in, or hadn't thought of. Fortunately, SPIN does include a general property-checking mechanism: If we can state our property in a particular formal temporal logic , then SPIN will allow us to check the property.

20. Execution Of TILCO Temporal Logic Specifications - Engineering Of Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://ieeexplore.ieee.org/iel5/8415/26521/01181500.pdf?arnumber=1181500

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