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{{Short description|Commonly used rules of replacement in propositional logic}} {{About|the rule of inference|the formula of absolute truth|Tautology (logic)|other uses|Tautology (disambiguation)}} ...

| field = [[Propositional calculus]] ...n because the term <math>Q</math> is "absorbed" by the term <math>P</math> in the [[consequent]].<ref>Whitehead and Russell, ''[[Principia Mathematica]]' ...

In [[mathematical logic]] and [[metalogic]], a [[formal system]] is called '''complete''' with resp ...al [[Validity (logic)|validity]]. Intuitively, a system is called complete in this particular sense, if it can derive every formula that is true. ...

{{Short description|Rule of replacement in propositional logic}} | field = [[Propositional calculus]] ...

{{Short description|Principle of classical logic}} ...port-export''' is a name given to the propositional form of [[Exportation (logic)|Exportation]]: ...

{{Short description|Axiom used in logic and philosophy}} ...l logic]]. It can be thought of as the [[law of excluded middle]] written in a form that involves only one sort of connective, namely implication. ...

...y in logic.<ref name=":0" /> The duality consists in these [[metalogic]]al theorems: ...ogic)|conjunction]] and [[Logical disjunction|disjunction]] can be defined in terms of each other, and consequently, only one of them needs to be taken a ...

...The characterization of standard complexity classes and correspondence to propositional proof systems allows to interpret theories of bounded arithmetic as formal ...Feasibility in Arithmetic, Jour. Symbolic Logic 36 (1971) 494–508.</ref> in 1971, and later developed by [[Samuel Buss|Samuel R. Buss]]. <ref name="bus ...

...nguish|text=the [[Gödel Prize]]}}{{Short description|Award in mathematical logic}} ...c|url=https://www.jstor.org/stable/2275205|journal=The Journal of Symbolic Logic|volume=57|issue=1|pages=352–365|doi=10.2307/2275205|issn=0022-4812|quote=Da ...

{{Short description|Symbolic logic system}} ...37}} It is an [[Intuitionistic logic|intuitionistic]] and [[paraconsistent logic]], that rejects both the [[law of the excluded middle]] as well as the [[pr ...

{{Short description|Extension of modal logic}} {{For|the subject in digital electronics also known as clocked logic|dynamic logic (digital electronics)}} ...

...stian cleric in red argues towards an older pensive white Christian cleric in black.]] ...britannica.com/topic/reductio-ad-absurdum|title=Reductio ad absurdum {{!}} logic|website=Encyclopedia Britannica|language=en|access-date=2019-11-27}}</ref>< ...

...Laws</ref> or between formulas themselves, for instance, in [[mathematical logic]]. For example, the formula <math>a^2 \geq 0</math> is true for all [[real with equality only in the degenerate case of a triangle with zero [[area]]. In [[Euclidean geometry]] and some other geometries, the triangle inequality i ...

...an output signal based on a threshold function. By connecting these units in various configurations, McCulloch and Pitts demonstrated that their model c ...ical theory of automata]''. In L. A. Jeffress (Ed.), ''Cerebral mechanisms in behavior; the Hixon Symposium'' (pp. 1–41). Wiley.</ref> ...

...the original DEL framework; more details about DEL in general can be found in the references. ...pistemology]]), [[economics]] ([[game theory]]) and [[cognitive science]]. In computer science, DEL is for example very much related to [[multi-agent sys ...

...ean algebra is therefore a formal way of describing [[logical operation]]s in the same way that elementary algebra describes numerical operations. ...d is provided for in all modern [[programming language]]s. It is also used in [[set theory]] and [[statistics]].<ref name="Givant-Halmos_2009"/> ...

{{short description|Study of the scope and nature of logic}} {{Distinguish|Philosophical logic}} ...

In [[order theory]] and [[model theory]], branches of mathematics, '''Cantor's ..., Cantor's original proof only used the "going forth" half of this method. In terms of [[model theory]], the isomorphism theorem can be expressed by sayi ...

...dered in antiquity, but some precursors of the concept can perhaps be seen in the work of medieval philosophers and mathematicians such as [[Oresme]]. ...nalysis]] by [[Weierstrass]] and others, the reformulation of [[geometry]] in terms of analysis, and the invention of [[set theory]] by [[Georg Cantor|Ca ...

{{Short description|Notable events in the history of geometry}} ...he other [[Vedic civilization|Vedic]] "[[Sulba Sutras]]" ("rule of chords" in [[Sanskrit]]) use [[Pythagorean triples]], contain a number of geometrical ...