Definitions for computability logic
com·putabil·i·ty log·ic

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1. computability logicnoun

   a formal theory of computability

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1. Computability logic

   Computability logic (CoL) is a research program and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic which is a formal theory of truth. It was introduced and so named by Giorgi Japaridze in 2003.In classical logic, formulas represent true/false statements. In CoL, formulas represent computational problems. In classical logic, the validity of a formula depends only on its form, not on its meaning. In CoL, validity means being always computable. More generally, classical logic tells us when the truth of a given statement always follows from the truth of a given set of other statements. Similarly, CoL tells us when the computability of a given problem A always follows from the computability of other given problems B1,...,Bn. Moreover, it provides a uniform way to actually construct a solution (algorithm) for such an A from any known solutions of B1,...,Bn. CoL formulates computational problems in their most general – interactive sense. CoL defines a computational problem as a game played by a machine against its environment. Such problem is computable if there is a machine that wins the game against every possible behavior of the environment. Such game-playing machine generalizes the Church-Turing thesis to the interactive level. The classical concept of truth turns out to be a special, zero-interactivity-degree case of computability. This makes classical logic a special fragment of CoL. Thus CoL is a conservative extension of classical logic. Computability logic is more expressive, constructive and computationally meaningful than classical logic. Besides classical logic, independence-friendly (IF) logic and certain proper extensions of linear logic and intuitionistic logic also turn out to be natural fragments of CoL. Hence meaningful concepts of "intuitionistic truth", "linear-logic truth" and "IF-logic truth" can be derived from the semantics of CoL. CoL systematically answers the fundamental question of what can be computed and how; thus CoL has many applications, such as constructive applied theories, knowledge base systems, systems for planning and action. Out of these, only applications in constructive applied theories have been extensively explored so far: a series of CoL-based number theories, termed "clarithmetics", have been constructed as computationally and complexity-theoretically meaningful alternatives to the classical-logic-based Peano arithmetic and its variations such as systems of bounded arithmetic. Traditional proof systems such as natural deduction and sequent calculus are insufficient for axiomatizing nontrivial fragments of CoL. This has necessitated developing alternative, more general and flexible methods of proof, such as cirquent calculus.

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1. Computability logic

   Introduced by Giorgi Japaridze in 2003, computability logic is a research programme and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic which is a formal theory of proof. In this approach logical formulas represent computational problems, and their validity means being "always computable". Computational problems and resources are understood in their most general - interactive sense. They are formalized as games played by a machine against its environment, and computability means existence of a machine that wins the game against any possible behavior by the environment. Defining what such game-playing machines mean, computability logic provides a generalization of the Church-Turing thesis to the interactive level. The classical concept of truth turns out to be a special, zero-interactivity-degree case of computability. This makes classical logic a special fragment of computability logic. Being a conservative extension of the former, computability logic is, at the same time, by an order of magnitude more expressive, constructive and computationally meaningful. Providing a systematic answer to the fundamental question "what can be computed?", it has a wide range of potential application areas. Those include constructive applied theories, knowledge base systems, systems for planning and action.

How to pronounce computability logic?

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How to say computability logic in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of computability logic in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of computability logic in Pythagorean Numerology is: 5

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Computability_Logic
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Computability_Logic
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=computability logic