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...escription|Inference rule that may be applied to only a particular segment of an expression}} {{Transformation rules}} ...

{{Short description|Rule of inference in predicate logic}} | type = [[Rule of inference]] ...

{{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)}} ...

{{Short description|Logical rule of inference}} | type = [[Rule of inference]] ...

| type = [[Rule of inference]] {{Transformation rules}} ...

{{Short description|Rule of inference in predicate logic}} | type = [[Rule of inference]] ...

...is a [[logical consequence|logical implication]] with an attached measure of uncertainty. ...of [[uncertainty]] of a document ''d'' to a query ''q'' be the probability of its logical implication, i.e.: ...

{{Short description|Rule of replacement in propositional logic}} | type = [[Rule of replacement]] ...

...ive''). The value restriction prevents reference cells from holding values of different types and preserves [[type safety]]. ...assignment) updates a reference to contain a new value and returns a value of the [[unit type]]. Given these, the following program<ref name=":0">{{Cite ...

...raic theories").<ref>equational logic. (n.d.). The Free On-line Dictionary of Computing. Retrieved October 24, 2011, from Dictionary.com website: http:// The terms of equational logic are built up from variables and constants using function s ...

...ast1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/ This inference has been argued to be [[validity (logic)|valid]] on the basis of sentence pairs such as that below, since Sentence 1 seems to imply Sentence ...

{{short description|Characteristic of some logical systems}} ...he property can be [[formal proof|derived]] using that system, i.e. is one of its [[theorem]]s; otherwise the system is said to be '''incomplete'''. ...

{{Short description|A less restrictive form of modal logic}} ...'' is a variant of [[modal logic]] that deviates from the basic principles of [[normal modal logic]]s. ...

...ated Constructor of Algorithms Handling More than Three Million Production Rules|class=cs.AI|eprint=1111.1321}}</ref> ...ogy Analysis for Various Intelligent Systems|journal=International Journal of Advanced Studies|language=en|volume=4|issue=4|pages=16|doi=10.12731/2227-93 ...

...ch is the [[convex hull]] of the risk points of the nonrandomised decision rules. ...|frequentist]] statistical theory sometimes requires the use of randomised rules to satisfy optimality conditions such as [[minimax]], most notably when der ...

...finite set of [[soundness|sound]] and implicationally complete [[inference rules]].<ref name=":3">{{Cite book |last=Krajicek |first=Jan |url=https://books.g ...2273702 |issn=0022-4812}}</ref> and was intended to capture the properties of the most common propositional proof systems.<ref name=":0" /> ...

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

...proofs were presented in tree-diagram form rather than in the tabular form of Suppes and Lemmon. Although the tree-diagram layout has advantages for phil ...<ref name=suppes1999 /> and Lemmon<ref name=lemmon1965 /> are applications of the tabular layout for teaching introductory logic. ...

It is applicable to a variety of [[machine learning]] problems, such as [[collective classification]], [[Rec PSL provides sophisticated inference techniques for finding the most likely answer (i.e. the [[Maximum_a_posteri ...

...ect-confuse|paradox of free choice|The Paradox of Choice{{!}}''The Paradox of Choice''}} ...itor-last1=Zalta |editor-first1=Edward |encyclopedia=Stanford Encyclopedia of Philosophy |title=Disjunction |url=https://plato.stanford.edu/archives/win2 ...