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Negation As Failure (NAF, for short) is a non-monotonic inference rule in logic programming, used to derive (i.e. that is assumed not to hold) from failure to derive . Note that n o t p {\displaystyle \mathrm {not} ~p} can be different from the statement ¬ p {\displaystyle \neg p} of the logical negation of p {\displaystyle p} , depending on ...
A model of a Datalog program P is an interpretation I of P which contains all the ground facts of P, and makes all of the rules of P true in I. Model-theoretic semantics state that the meaning of a Datalog program is its minimal model (equivalently, the intersection of all its models). [4] For example, this program:
In Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or.That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false.
As a further example, negation can be defined in terms of NAND and can also be defined in terms of NOR. Algebraically, classical negation corresponds to complementation in a Boolean algebra, and intuitionistic negation to pseudocomplementation in a Heyting algebra. These algebras provide a semantics for classical and intuitionistic logic.
Examples: 0 or 0 = 0; 0 or 1 = 1; 1 or 0 = 1; 1 or 1 = 1; 1010 or 1100 = 1110; The or operator can be used to set bits in a bit field to 1, by or-ing the field with a constant field with the relevant bits set to 1. For example, x = x | 0b00000001 will force the final bit to 1, while leaving other bits unchanged. [citation needed]
Logical connectives can be used to link zero or more statements, so one can speak about n-ary logical connectives. The boolean constants True and False can be thought of as zero-ary operators. Negation is a unary connective, and so on.
The concept of a stable model, or answer set, is used to define a declarative semantics for logic programs with negation as failure.This is one of several standard approaches to the meaning of negation in logic programming, along with program completion and the well-founded semantics.
Prolog is a logic programming language that has its origins in artificial intelligence, automated theorem proving and computational linguistics. [1] [2] [3]Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is intended primarily as a declarative programming language: the program is a set of facts and rules, which define relations.