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{{Short description|Digital logic gate}} The '''IMPLY gate''' is an informal digital [[logic gate]] that implements a [[logical conditional]]. ...

{{Short description|Digital logic gate}} The '''NIMPLY gate''' is a digital [[logic gate]] that implements a [[material nonimplication]]. ...

...le]]s.<ref>L. Henkin. ''Logical systems containing only a finite number of symbols'', Report, Department of Mathematics, University of Montreal, 1967</ref> Th ...ion Problem for Two-Variable First-Order Logic'', The Bulletin of Symbolic Logic, Vol. ...

In [[logic]] and [[model theory]], a '''valuation''' can be: *In [[propositional logic]], an assignment of [[truth value]]s to [[propositional variable]]s, with a ...

In [[logic]], the [[symbol (formal)|symbol]] ⊨, ⊧ or <math>\models</math> is called th ...gicproject.org/content/first-order-logic/first-order-logic.pdf First-order logic] (p.7). Accessed 4 January 2022.</ref> ...

...Dictionary.com website: http://dictionary.reference.com/browse/equational+logic</ref> ...equational logic are built up from variables and constants using function symbols (or operations). ...

...mathematical logic)|formula]] is the depth of nesting of its [[Quantifier (logic)|quantifiers]]. It plays an essential role in [[model theory]]. * We write FO[n] for the set of all [[First-order logic|first-order]] formulas φ with <math>qr(\varphi) \le n</math>. ...

...axioms#Models|standard model]] of the [[Peano axioms]] in the [[Signature (logic)|language]] of the first-order Peano axioms. ...ols together with the logical symbols in the usual manner of [[first-order logic]]. ...

...c]] due to [[Skolem]] that is [[proof-theoretic]]ally tractable. Geometric logic is capable of expressing many mathematical theories and has close connectio A theory of first-order logic is geometric if it is can be axiomatised using only axioms of the form ...

...ry of logic|dominant connective}} and {{glossary link|glossary=Glossary of logic|subordinate connective}} are defined in terms of whether a connective inclu ...books.google.com/books?id=38LCAgAAQBAJ |title=First Course in Mathematical Logic |last2=Hill |first2=Shirley |date=April 30, 2012 |publisher=Courier Corpora ...

...h inductive definitions |journal=International Conference on Computational Logic |date=2000 |pages=703–717 |doi= |arxiv=cs/0003019 |bibcode=2000cs........30 ...ve Logic Programming: Theory, Systems, and Applications |chapter=Predicate logic as a modeling language: The IDP system |date=2018 |pages=279–323 |doi=10.11 ...

...t all.<ref>{{Cite book| last1=Monk | first1=J. Donald | title=Mathematical Logic | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Gradua ...cation over predicates and whose signature extends to monadic second-order logic of ''k'' successors<ref>{{cite journal |last1=Rabin |first1=Michael O. |tit ...

...tern. In the case where an argument pattern has multiple adjacent variable symbols, the argument pattern will match any and all partitions of the actual value ...

...eory|first-order set theory]] in which the language uses only a [[googol]] symbols or less.</blockquote> ...of first-order set-theory with less than a googol (<math>10^{100}</math>) symbols."<ref name="tech" /> ...

{{Short description|Concept in mathematical logic}} ...iable over the integers. The dual concept to satisfiability is [[Validity (logic)|validity]]; a formula is ''valid'' if every assignment of values to its va ...

...rrow''' and the expression x ↦ y is called a '''maplet'''. In [[separation logic]] it denotes the contents of a specific cell of memory. [[Category:Mathematical symbols]] ...

...'''end extension''' of <math>\mathfrak{A}=\langle A, E\rangle </math>, in symbols <math>\mathfrak{A}\subseteq_\text{end}\mathfrak{B}</math>, if | title=Logic Year 1979–80 ...

{{Short description|Concept of logic or linguistics}} In [[logic]] and [[linguistics]], an expression is '''syncategorematic''' if it lacks ...

...ebraic Theory of Context-Free Languages* |date=1959-01-01 |work=Studies in Logic and the Foundations of Mathematics |volume=26 |pages=118–161 |editor-last=B A '''homomorphism''' is based on a function <math>h</math> which maps symbols from an alphabet <math>\Gamma</math> to words over another alphabet <math>\ ...

...ts (of zero arity) are also called '''constants'''. Terms built with unary symbols and constants can be considered as [[string (computer science)|strings]]. H ...