Temporal logic

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Temporal logics or time logics are extensions of the logic through which temporal processes can be recorded. They are applications of modal logic based on a before-and-after relationship between points in time. Whether this results in a dense or discrete time order depends on the determination of this relation.

General

The philosophical foundations of temporal logics were developed by Arthur Norman Prior and John McTaggart . The two most important model families of time logic are linear temporal logic (LTL) and computation tree logic (CTL). While LTL assumes a linear sequence of points in time, CTL describes a branching time sequence. Because both logics can describe different facts, but also have a large overlap, one defines CTL * of which both CTL and LTL are a subset.

Atemporal logic such as propositional logic cannot, or only with great difficulty, adequately handle statements whose truth values ​​change over time. “It is raining” is only true if it is raining at the time and location, otherwise not. Classical atemporal logics therefore count the utterance time to the truth conditions (a case of “It's raining” is uttered at a certain point in time and is true if it rains at this point in time). Each case of the utterance of the proposition thus has its own truth conditions. In contrast, time logics introduce modal operators so that every case of the utterance of the sentence is subject to the same truth conditions. These operators make it possible to logically analyze differentiated temporal statements, so that “It has rained”, “It will rain”, “It is always raining” is truth-functionally dependent on the fulfillment of “It is raining” at certain times.

The computer scientist Amir Pnueli introduced temporal logic into the test systematics of large and complex EDP systems and thus described reproducible and comparable states in programs and thus test criteria.

In dialogical logic , a framework for temporal logic is introduced in such a way that a statement made early in the dialog game is no longer available later in the dialog.

literature

  • Jürgen Dassow: Logic for computer scientists . Vieweg & Teubner 2005, ISBN 3519005182 , pp. 125ff
  • Runggaldier, Edmund: Formal semantic renewal of metaphysics. In: Matthias Lutz-Bachmann (ed.): Metaphysics Today - Problems and Perspectives of Ontology. Alber, Freiburg 2007, p. 57 (67–72) (“Continuants and Time”, “Time Logic and the Problem of the Now”, “A and B Series” ( John McTaggart Ellis McTaggart )).
  • Arthur Prior: Time and Modality. Oxford University Press 1957
  • John McTaggart Ellis McTaggart: The Unreality of Time . In: Min. A Quarterly Review of Psychology and Philosophy 17/1908, pp. 457-474. (German translation: The unreality of time. In: Walther Ch. Zimmerli and Mike Sandbothe: Classics of modern philosophy of time . Scientific book society, Darmstadt 1993, pp. 67-86).
  • Dov M. Gabbay, Mark A. Reynolds, Marcelo Finger: Temporal Logic - Mathematical Foundations and Computational Aspects - Volume 2 ; Clarendon Press Oxford 2000; ISBN 0-19-853768-9

See also

Web links