The temporal logic of actions

Lamport, Leslie

doi:10.1145/177492.177726

Cited by 1,287 publications

(721 citation statements)

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“…Although I have carried out the verification using a simple version of the I/O automaton model, it is probably trivial to translate this story to other state based models, such as Lamport's Temporal Logic of Actions [8].…”

Section: Discussionmentioning

confidence: 99%

Verification of a distributed summation algorithm

Vaandrager

1995

CONCUR '95: Concurrency Theory

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Section: Discussionmentioning

confidence: 99%

Verification of a distributed summation algorithm

Vaandrager

1995

CONCUR '95: Concurrency Theory

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“…This presupposes the adequacy of mathematical abstractions specifically invented or adopted and elaborated for the expression of more sophisticated modalities of time's now than those currently used in such formalisms as temporal logic (e.g. TLA, Lamport, 1994;. There is much to be explored in what other languages and cultures deliver to physics (e.g.…”

Section: Epiloguementioning

confidence: 99%

Yet another time about time … Part I: An essay on the phenomenology of physical time

Simeonov¹

2015

Progress in Biophysics and Molecular Biology

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This paper presents yet another personal reflection on one the most important concepts in both science and the humanities: time. This elusive notion has been not only bothering philosophers since Plato and Aristotle. It goes throughout human history embracing all analytical and creative (anthropocentric) disciplines. Time has been a central theme in physical and life sciences, philosophy, psychology, music, art and many more. This theme is known with a vast body of knowledge across different theories and categories. What has been explored concerns its nature (rational, irrational, arational), appearances/qualia, degrees, dimensions and scales of conceptualization (internal, external, fractal, discrete, continuous, mechanical, quantum, local, global, etc.). Of particular interest have been parameters of time such as duration ranges, resolutions, modes (present, now, past, future), varieties of tenses (e.g. present perfect, present progressive, etc.) and some intuitive, but also fancy phenomenological characteristics such as "arrow", "stream", "texture", "width", "depth", "density", even "scent". Perhaps the most distinct characteristic of this fundamental concept is the absolute time constituting the flow of consciousness according to Husserl, the reflection of pure (human) nature without having the distinction between exo and endo. This essay is a personal reflection upon time in modern physics and phenomenological philosophy.Keywords: space, time, consciousness, physics, mathematics, philosophy, phenomenology. ___________________________________________________________________ PrologueSpace and time are particularly modalities of human consciousness. Whereas space can be realized through our eyes and limbs, time remains elusive to our minds and still bothers philosophers since antiquity (Dyke & Bardon, 2013). In the beginning of the 20 th century science made a crucial switchover. Time was spatialized 1 . Until then the world was threedimensional. With the Special Relativity Theory (Einstein, 1905;Minkowski, 1909) the concept of time became the fourth dimension 2 and an integral element of the new physical worldview. It caused confusion among many of Einstein's contemporaries, and not only with its relativistic dilation in the well-known equation with the speed of light ť = t (1-(v/c) 2 ) ½ .1 It could be argued that time was spatialized earlier. Though time and space were separate for Newton (something that Einstein challenged), the clock time he assumed was laid out like space and was devoid of the dynamism of Bergsonian durée, (Bergson, 1912;Čapek, 1961). 2 It was Laplace who treated time as just another dimension equivalent to space, and thereby paved the way for the development of relativity theory as it came to be understood (but not as Čapek, following Bergson, understood it).This notion of relativistic time appeared wrong and unnatural, not without good reason, since:• Time is ineffable, eluding science and mathematics: it can only be grasped through intuition and shown indirectly and partia...

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“…However, Lamport [10] has identified a shortcoming of standard linear-time temporal logic (LTL): because it is based on a global notion of "next state", it does not allow to relate specifications written at different levels of abstraction. He has therefore maintained that specifications should be invariant under "stuttering", that is, finite repetitions of identical states, and has proposed the Temporal Logic of Actions (TLA) [12,13,6]. Characteristically, TLA formulas contain the "next-time" operator only in a restricted form and can therefore not distinguish between stuttering-equivalent behaviors.…”

Section: Introductionmentioning

confidence: 99%

A more complete TLA

Merz¹

1999

FM’99 — Formal Methods

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Abstract. This paper defines a generalization of Lamport's Temporal Logic of Actions. We prove that our logic is stuttering-invariant and give an axiomatization of its propositional fragment. We also show that standard TLA is as expressive as our extension once quantification over flexible propositions is added. BackgroundTemporal logics are routinely used for the specification and analysis of reactive systems. However, Lamport [10] has identified a shortcoming of standard linear-time temporal logic (LTL): because it is based on a global notion of "next state", it does not allow to relate specifications written at different levels of abstraction. He has therefore maintained that specifications should be invariant under "stuttering", that is, finite repetitions of identical states, and has proposed the Temporal Logic of Actions (TLA) [12,13,6]. Characteristically, TLA formulas contain the "next-time" operator only in a restricted form and can therefore not distinguish between stuttering-equivalent behaviors. Several case studies have established TLA as a useful formalism for describing systems; on the theoretical side, researchers have studied questions such as the description of real-time and hybrid systems [3,11], the representation of assumption-commitment reasoning [4,5], and the expressiveness of propositional TLA [18]. Moreover, Lamport has developed a formal specification language TLA+ based on TLA.Although TLA has been found to be expressively complete for stuttering-invariant ω-regular languages [18], this does not necessarily imply that specifications can be expressed in a natural way. In fact, the syntactic restrictions imposed by Lamport that ensure invariance under stuttering occasionally make it hard to express seemingly simple properties. For example, whereas the requirement "eventually P will be true, and Q will hold at some later state" is expressed by the formula 3(P ∧ 3Q), as in standard LTL, the analogous requirement "eventually action A will be performed, some time later followed by action B" is not expressed as easily. Eventual occurrence of action A is expressed by the formula 3 A v , where A describes the action as a relation on pairs of states, and v is (roughly speaking) the tuple of all state components of interest. One might therefore expect to express the informal requirement above by a formula such as 3 A ∧ 3 B v v , but TLA does not allow temporal formulas to occur inside an action formula (i.e., inside angle brackets). In some cases one can identify a state formula pA that is true iff action A has happened sometime in the past: for example, A might represent a request for a resource, and pA could be defined from the system's logfile. In those cases, we can express our requirement by the formula 3 pA ∧ B v . This

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The temporal logic of actions

Cited by 1,287 publications

References 17 publications

Verification of a distributed summation algorithm

Verification of a distributed summation algorithm

Yet another time about time … Part I: An essay on the phenomenology of physical time

A more complete TLA

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