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The system of all truth constants in the language is supposed to satisfy the bookkeeping axioms: [9] & ¯ (¯ & ¯), ¯ (¯ ¯), etc. for all propositional connectives and all truth constants definable in the language. Involutive negation (unary) can be added as an additional negation to t-norm logics whose residual negation is not itself ...
Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...
Pages in category "Articles with example Python (programming language) code" The following 200 pages are in this category, out of approximately 201 total. This list may not reflect recent changes. (previous page)
In C (and some other languages descended from C), double negation (!!x) is used as an idiom to convert x to a canonical Boolean, ie. an integer with a value of either 0 or 1 and no other. Although any integer other than 0 is logically true in C and 1 is not special in this regard, it is sometimes important to ensure that a canonical value is ...
Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic . In contrast to the latter, the core reasoning problems for DLs are (usually) decidable , and efficient decision procedures have been designed and implemented for ...
In a dagger category , a morphism is called . unitary if † =,; self-adjoint if † =.; The latter is only possible for an endomorphism:.The terms unitary and self-adjoint in the previous definition are taken from the category of Hilbert spaces, where the morphisms satisfying those properties are then unitary and self-adjoint in the usual sense.
If S is a commutative semigroup then the identity map of S is an involution.; If S is a group then the inversion map * : S → S defined by x* = x −1 is an involution. Furthermore, on an abelian group both this map and the one from the previous example are involutions satisfying the axioms of semigroup with involution.
A literal is a propositional variable or the negation of a propositional variable. Two literals are said to be complements if one is the negation of the other (in the following, is taken to be the complement to ). The resulting clause contains all the literals that do not have complements. Formally: