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Topic: Temporal logic

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Logic

Modal logic

Provability logic

List of topics in logic

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Mathematical logic

Semantics

Reification

	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 terms of time.
		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 views time as a sequence of states is a temporal logic, and any logic which uses only two truth values is a binary logic.
	en.wikipedia.org /wiki/Temporal_logic (467 words)

	Modal logic - Wikipedia, the free encyclopedia
		Logics for handling a number of other ideas, such as eventually, formerly, can, could, might, may, must are by extension also called modal logics, since it turns out that these can be treated in similar ways.
		Logical possibility is a form of alethic possibility; (4) makes a claim about whether it is possible for a mathematical truth to have been false, but (3) only makes a claim about whether it is possible that the mathematical claim turns out false, for all Jones knows, and so again Jones does not contradict himself.
		Significantly, modal logics can be developed to accommodate most of these idioms; it is the fact of their common logical structure (the use of "intensional" or non-truth-functional sentential operators) that make them all varieties of the same thing.
	en.wikipedia.org /wiki/Modal_logic (3184 words)

	Abstracts
		Temporal logic is used to specify constraints that restrict the simulation to a region of the state space and to specify trajectories for input variables.
		A propositional linear--time temporal logic is adopted, which is extended to a three valued logic that allows a formula to be conditionally entailed when quantitative information specified in the formula can be applied to a behavior to refine it.
		Temporal logic expressions are used to specify constraints that restrict the simulation to a region of the state space and to specify trajectories for input variables.
	www.cs.utexas.edu /users/qr/abstracts-tl.html (1297 words)

	Modal Logic
		Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’.
		Deontic logics introduce the primitive symbol O for ‘it is obligatory that’, from which symbols P for ‘it is permitted that’ and F for ‘it is forbidden that’ are defined: PA = ~O~A and FA = O~A. The deontic analog of the modal axiom (M): OA→A is clearly not appropriate for deontic logic.
		In deontic logic, temporal logic, and others, the analog of the truth condition (5) is clearly not appropriate; furthermore there are even conceptions of necessity where (5) should be rejected as well.
	plato.stanford.edu /entries/logic-modal (7308 words)

	Temporal Logic
		Tense Logic was introduced by Arthur Prior (1957, 1967, 1969) as a result of an interest in the relationship between tense and modality attributed to the Megarian philosopher Diodorus Cronus (ca.
		This kind of manoeuvre lies at the heart of hybrid temporal logics in which the standard apparatus of propositions and tense operators is supplemented by propositions which are true at unique instants, thereby effectively naming those instants without invoking philosophically dubious reification.
		Prior's motivation for inventing Tense Logic was largely philosophical, his idea being that the precision and clarity afforded by a formal logical notation was indispensible for the careful formulation and resolution of philosophical issues concerning time.
	plato.stanford.edu /entries/logic-temporal (3508 words)

	Diagnosing Java code: Assertions and temporal logic in Java programming
		Temporal logic is a formalism used to describe how a program state will change with time.
		Temporal logic is a type of modal logic that is used for reasoning about changing properties with time.
		Temporal Rover, from Time Rover Inc., is a tool for processing temporal logic assertions in Java programs and generating valid Java code from the assertions.
	www-128.ibm.com /developerworks/java/library/j-diag0723.html?loc=j (1979 words)

	Temporal Logic Case Study
		Wood, W. 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.
	www.sei.cmu.edu /publications/documents/89.reports/89.tr.024.html (131 words)

	Diagnosing Java code: Using temporal logic with bug patterns
		Temporal logic assertions are also useful for diagnosing such errors in the first place.
		One of the most straightforward applications of temporal logic assertions is for adding executable documentation on interfaces, thereby catching fictitious implementations of the interface as soon as these assertions are violated.
		Not only are the temporal logic assertions in the interface much more precise than prose would be, but they are actually enforced at run time (if we are running code instrumented to include checks on the assertions).
	www.ibm.com /developerworks/library/j-diag0827.html (2161 words)

	Combining Temporal Logic Systems, Marcelo Finger, Dov Gabbay
		Four combination methods are described and studied with respect to the transfer of logical properties from the component one-dimensional temporal logics to the resulting combined two-dimensional temporal logic.
		Each combination method comprises three submethods that combine the languages, the inference systems, and the semantics of two one-dimensional temporal logic systems, generating families of two-dimensional temporal languages with varying expressivity and varying degrees of transfer of logical properties.
		The temporalization method and the independent combination method are shown to transfer all three basic logical properties.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.ndjfl/1040046087 (652 words)

	Basic temporal logic
		Accordingly, the minimal temporal logic is axiomatized by adding to system K the axiom (4), which corresponds to transitivity.
		indicating that a temporal logic is being considered.
		More complex logics of time are usually developed on the basis of richer languages.
	www.informatik.uni-leipzig.de /~duc/Thesis/node52.html (172 words)

	Modal Logic (Site not responding. Last check: 2007-10-08)
		Temporal necessity: Since Camile was born in 1985, she must be at least 14 years old.
		Temporal logic plays an important role in the specification, derivation, and verification of programs as programs may be viewed as progressing through a sequence of states, a new state after each event in the system.
		The propositional modal logics share with classical propositional logic the finite model property; if a collection of formulas is satisfiable, it is satisfiable in a finite graph.
	cs.wwc.edu /~aabyan/Logic/Modal.html (2554 words)

	Modal Temporal Logic (Site not responding. Last check: 2007-10-08)
		Research into temporal logic includes the study of temporal logic within the framework of logic and covers: axiom systems, theorem proving and proof theory, model theory, execution models and applications.
		The efficiency of the execution stems from viewing temporal evaluations as temporal constraints on intervals end points and generating maximal intervals at which formulae holds.
		Investigation of theorem proving for modal temporal logic led to the development of a non-clausal theorem prover for first order temporal logic.
	www.comp.brad.ac.uk /research/ai/temporal.html (181 words)

	Alur/Henzinger/Kupferman: Alternating-time Temporal Logic (Site not responding. Last check: 2007-10-08)
		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.
		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.
	www-cad.eecs.berkeley.edu /~tah/Publications/alternating-time_temporal_logic.html (394 words)

	Existential Graphs and Tense Logic
		In the logic of relatives, choice has to be made between different lines of reasoning equally logical and equally direct.
		If tense logical systems are to be represented in a proper Peircean manner, there can little doubt that one ought to make the attempt in terms of the existential graphs which Peirce invented in 1896 and which he continued developing in the following years.
		For logical investigation is very slow, involving as it does the taking up of a confused mass of ordinary ideas, embracing we know not what and going through with a great quantity of analyses and generalizations and experiments before one can so much as get a new branch fairly inaugurated.
	www.hum.aau.dk /~poe/ARTIKLER/tense_graphs.html (4044 words)

	Temporal Logic (Site not responding. Last check: 2007-10-08)
		Temporal logics are used to predicate over the behavior defined by Kripke structures.
		Two useful temporal logics are Computation Tree Logic (called CTL) and Linear Temporal Logic (called LTL).
		In CTL temporal operators it is possible to quantify over the paths departing from a given state.
	nusmv.irst.itc.it /NuSMV/papers/sttt_j/html/node3.html (378 words)

	Logical consecutions in discrete linear temporal logic , V. V. Rybakov
		We investigate logical consequence in temporal logics in terms of logical consecutions, i.e., inference rules.
		The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈 𝒵, ≮, ≤ 〉 of all integer numbers, is the prime object of our investigation.
		Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.jsl/1129642119 (675 words)

	Temporal logic (Site not responding. Last check: 2007-10-08)
		Temporal logic is ordinary logic extended with temporal operators [] (read henceforth) and
		Temporal logic, as it has been defined here, cannot formally specify things like average response time and probability of failure.
		As an example of temporal specifications and safety and liveness specifications in particular, we provide a specification of the The Dining Philosophers Problem.
	moonbase.wwc.edu /~aabyan/TL (583 words)

	BRICS Lecture Series, Abstracts, 1997 (Site not responding. Last check: 2007-10-08)
		Abstract: Temporal logic is obtained by adding temporal connectives to a logic language.
		In this chapter, we survey the fundamental varieties of temporal logic and describe their applications in information systems.
		Temporal logic queries can be translated to an algebraic language.
	www.brics.dk /LS/97/Abs/BRICS-LS-97-Abs (209 words)

	Oxford University Press
		This long awaited book gives a thorough account of the mathematical foundations of temporal logic, one of the most important logic areas in computer science.
		It gives a solid introduction to semantical and axiomatic approaches to temporal logic, and covers the central topics of predicate temporal logic, metalanguages, general theories of axiomatization, many dimensional systems, propositional quantifiers, expressive power, Henkin dimension, temporalization of other logics, and decidability results.
		Temporal logics presented in the predicate calculus: language-metalanguage
	www.oup.com /ca/isbn/0-19-853769-7 (467 words)

	Informit Safari Tech Books Online - A Practical Guide to Testing Object-Oriented Software
		We have found that interval temporal logic is useful in expressing temporal relationships.
		The operators of temporal logic allow concepts of time ordering to be expressed and reasoned about.
		Interval temporal logic allows concepts about time periods, as opposed to specific points in time, to be expressed.
	safari.informit.com /?x=1&mode=section&sortKey=rank&sortOrder=desc&view=book&xmlid=0-201-32564-0/ch08lev1sec10&open=false&g=&catid=&s=1&b=1&f=1&t=1&c=1&u=1&r=&o=1 (305 words)

	Specification of Distributed Systems - An Object-Oriented Approach Combining Temporal Logic and Rewriting Logic (Site not responding. Last check: 2007-10-08)
		Maude integrates an equational style of functional specification in its equational logic sublanguage with an object-oriented specification style for object systems that can be highly concurrent and nondeterministic.
		Rewriting logic is primarily a logic of change in which the deduction directly corresponds to the change.
		By contrast, temporal logic is a logic to talk about change in a global way.
	www-linguistics.stanford.edu /Linguistics/llc/abs98/denker/denker.html (250 words)

	Specifications in Temporal Logic (Site not responding. Last check: 2007-10-08)
		Temporal logic studies the structure or topology of time [13].
		In more recent years, temporal logic has been successfully applied in various areas of computer science, especially software verification.
		RTTL is an extension of the Manna-Pnueli temporal logic [11].
	rutcor.rutgers.edu /~pinzon/papers/rrr1/node13.html (245 words)

	Logical Consecutions in Intransitive Temporal Linear Logic of Finite Intervals -- Rybakov 15 (5): 663 -- Journal of ...
		Logical Consecutions in Intransitive Temporal Linear Logic of Finite Intervals -- Rybakov 15 (5): 663 -- Journal of Logic and Computation
		Logical Consecutions in Intransitive Temporal Linear Logic of Finite Intervals
		temporal consecutions and prove that the class of admissible
	logcom.oxfordjournals.org /cgi/content/abstract/15/5/663 (148 words)

	Linear Temporal Logic (Site not responding. Last check: 2007-10-08)
		Temporal operators are implemented as inductive (respectively co-inductive) types when they are least (respectively greatest) fixpoints.
		Program executions are represented by infinite co-inductive lists and temporal operators by co-inductive or inductive types, depending on whether they are greatest or least fixpoints.
		It makes it possible to conclude that, provided that a property A initially holds on a stream, a property B continuously holds until a property C is eventually satisfied.
	coq.inria.fr /contribs/LTL.html (243 words)

	Zohar Manna's home page
		The STeP (Stanford Temporal Prover) system supports the computer-aided formal verification of reactive, real-time and hybrid systems based on their temporal specification.
		The Temporal Logic of Reactive and Concurrent Systems:Specification Springer-Verlag, 1992.
		The course also places emphasis on temporal logics, their expressive power and the applications of automata theory in formal methods.
	theory.stanford.edu /people/zm (271 words)

	Temporal Massage Parlor (Site not responding. Last check: 2007-10-08)
		Optimized Translator of an Extended Linear Temporal Logic into Büchi automata and Promela (the input language of the SPIN model checker).
		The translator employs a number of optimizations in order to "massage" temporal formulas into small Büchi automata.
		"Stutter-invariant languages, omega-automata, and Temporal Logic", Proceedings of 11th Conference on Computer-Aided Verification, pp.
	www.bell-labs.com /project/TMP (159 words)

	Publications
		Temporal Triggers in Active Databases (with Ouri Wolfson), IEEE Transactions on Knowledge and Data Engineering, Vol 7, No 3, June 1995.
		On the Eventuality Operator in Temporal Logic (with Lenore Zuck), Proceedings of the second IEEE Symposium On Logic in Computer Science, Cornell University, Ithaca, June 1987.
		Using Temporal Logic for Automatic Verification of Finite State Systems (with M.Browne, E.M.Clarke and E.A.Emerson), Proceedings of the Advanced Course "Logics and Models for Verifications and Specifications of Concurrent Systems", Colle-sur-Loup, France, October 1984, Also Appeared in Springer-verlag Lecture Notes in Computer Science.
	www.cs.uic.edu /~sistla/publications.html (1804 words)

	Verifying Temporal Formulas in the Temporal Logic of Actions
		The goal of the project was to extend TLC to verify arbitrary temporal formulas.
		The problem of verifying arbitrary temporal formulas about states is a standard one, addressed by other model-checkers as well.
		But the Temporal Logic of Actions actually allows even greater generality -- it allows arbitrary temporal formulas involving actions and states.
	gatekeeper.dec.com /pub/DEC/SRC/technical-notes/SRC-1999-003-html/wischik.html (735 words)

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