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Where ψ and φ represent formulas of propositional logic, ψ is a substitution instance of φ if and only if ψ may be obtained from φ by substituting formulas for propositional variables in φ, replacing each occurrence of the same variable by an occurrence of the same formula. For example: ψ: (R → S) & (T → S) is a substitution ...
W.V.O. Quine takes substitutivity salva veritate to be the same as the "indiscernibility of identicals". Given a true statement, one of its two terms may be substituted for the other in any true statement and the result will be true. [2]
Given a goal clause, represented as the negation of a problem to be solved : with selected literal , and an input definite clause: . whose positive literal (atom) unifies with the atom of the selected literal , SLD resolution derives another goal clause, in which the selected literal is replaced by the negative literals of the input clause and the unifying substitution is applied:
For example, using x,y,z as variables, and taking f to be an uninterpreted function, the singleton equation set { f(1,y) = f(x,2) } is a syntactic first-order unification problem that has the substitution { x ↦ 1, y ↦ 2 } as its only solution. Conventions differ on what values variables may assume and which expressions are considered ...
For example, oxygen is necessary for fire. But one cannot assume that everywhere there is oxygen, there is fire. A condition X is sufficient for Y if X, by itself, is enough to bring about Y. For example, riding the bus is a sufficient mode of transportation to get to work.
Propositional logic deals with statements, which are defined as declarative sentences having truth value. [29] [1] Examples of statements might include: Wikipedia is a free online encyclopedia that anyone can edit. London is the capital of England. All Wikipedia editors speak at least three languages.
The gambling industry, much like AI, is in the middle of an unprecedented gold rush. In 2018, a US Supreme Court ruling allowed states to legalize sports betting; nearly 40 states since did ...
Order-sorted logic can be translated into unsorted logic, using a unary predicate () for each sort , and an axiom (() ()) for each subsort declaration . The reverse approach was successful in automated theorem proving: in 1985, Christoph Walther could solve a then benchmark problem by translating it into order-sorted logic, thereby boiling it ...