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...ally tractable. Geometric logic is capable of expressing many mathematical theories and has close connections to [[topos theory]]. ...rst-order logic is geometric if it is can be axiomatised using only axioms of the form ...

...ple of explosion]] (''ex falso quodlibet''), and therefore holding neither of the following two derivations as valid: ...any propositions. Most constructive logics only reject the former, the law of excluded middle. In classical logic, the ''ex falso'' laws ...

...ula, then any ''x'' such that ''P''(''x'') = ''A'' is called a ''P''-proof of ''A''. The condition defining pps can be broken up as follows: ...If ''P'' accepts the pair (''A'',''x'') we say that ''x'' is a ''P''-proof of ''A''. ''P'' is required to run in polynomial time, and moreover, it must h ...

...ies for creating a new type from constants and functions that create terms of that type. The feature serves a role similar to [[data structure]]s in a p ...iven a proof of "P 0" and a proof of "P n -> P (n+1)", we get back a proof of "forall n, P n". This is the familiar induction principle for natural numbe ...

{{For|solving systems of inequalities|Dis-unification}} '''Anti-unification''' is the process of constructing a generalization common to two given symbolic expressions. As ...

{{short description|Determining the probability of future events based on past events}} ...ical basis for [[learning]] and the perception of patterns. It is a source of [[knowledge]] about the world. ...

...ioms. While some are [[Mathematics|mathematically]] equivalent to [[Theory of relativity|Einstein's theory]], others aim to revise or extend it. ...metry of [[spacetime]] and the [[linear transformation]]s between [[frames of reference]]. ...

| caption = Portrait of Dan E. Willard for the 2008 University at Albany President’s Award for Exce ...}}</ref>) was an American computer scientist and logician, and a professor of computer science at the [[University at Albany]]. ...

...ture]] that stores an [[equivalence relation]] over [[Term (logic)|terms]] of some language. ...at may be compared for equality, called '''e-class IDs'''. The application of <math>f\in\Sigma_n</math> to e-class IDs <math>i_1, i_2, \ldots, i_n\in\mat ...

...antics]] for defined expressions, and formal proof systems study the logic of circular expressions. ...l]] and philosophical logic. It has been used to provide circular analyses of philosophical and logical concepts. ...

...e., a [[small-step operational semantics]] with an explicit representation of the reduction context—more efficiently. It is a step towards implementing ...reductions that starts with <math>p_0</math> and continues with a sequence of reducts <math>p_i</math>, where <math>i > 0</math>: ...

...of the noise statistics on the field values, and partly unknown parameters of measurement. For this it uses [[Feynman diagrams]], [[renormalisation]] flo ...nto the field inference in order to overcome the mismatch of field degrees of freedom to measurement points. To handle this, an information theory for fi ...

...[[wikt:doxastic|doxastic]] attitude. For example, a perceptual experience of a tree may serve as evidence to justify the belief that there is a tree. In ...[[theory-ladenness]] are two obstacles that threaten to undermine the role of scientific evidence. ...

{{Not to be confused with|Marxism}}{{Short description|School of economic thought}} ...ocialist construction in the Soviet Union, contributing to the development of Soviet [[Political economy|Political Economy]]. ...

{{short description|Study of the scope and nature of logic}} ...to the philosophy of logic as the discipline investigating the properties of formal logical systems, like [[consistency]] and [[Completeness (logic)|com ...

{{Short description|Mathematical use of "for all" and "there exists"}} ...ound variable]] and a [[subformula]] specifying a property of the referent of that variable. ...

{{Short description|Study of correct reasoning}} {{About|the study of correct reasoning||Logic (disambiguation)|and|Logician (disambiguation)}} ...

...[[chemical potential]] across a curved surface or interface. The existence of a positive interfacial energy will increase the energy required to form sma ...th their liquid, melt at a lower temperature than large crystals. In cases of confined geometry, such as liquids contained within porous media, this lead ...

{{Short description|Sub-field of reinforcement learning}} [[File:Magent-graph-2.gif|thumb|Two rival teams of agents face off in a [https://github.com/Farama-Foundation/MAgent#readme MA ...

...ry sources|date=February 2025}}{{Quantum mechanics|cTopic=[[Interpretation of quantum mechanics|Interpretations]]}} ...n]] as the [[Kolmogorov equations|Kolmogorov equation]] for a certain type of conservative (or unitary) diffusion.{{sfn|Nelson |1966}}{{sfn|Nelson |1985} ...