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The situation calculus is a logic formalism designed for representing and reasoning about dynamical domains. It was first introduced by John McCarthy in 1963. [1] The main version of the situational calculus that is presented in this article is based on that introduced by Ray Reiter in 1991.
The difference between a predicate and a term in first-order logic is that a term is a representation of an object (possibly a complex object composed of other objects), while a predicate represents a condition that can be true or false when evaluated over a given set of terms.
A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0-arity) predicates.
For predicate logic, the atoms are predicate symbols together with their arguments, each argument being a term. According to some terminology, an open formula is formed by combining atomic formulas using only logical connectives, to the exclusion of quantifiers. [15] This is not to be confused with a formula which is not closed.
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.
The early development of logic programming was largely a European phenomenon. In North America, AI researchers such as Ed Feigenbaum and Frederick Hayes-Roth advocated the representation of domain-specific knowledge rather than general-purpose reasoning. [5]
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information.
It essentially allows a certain kind of reduction of first-order logic to propositional logic. Herbrand's theorem is the logical foundation for most automatic theorem provers . Although Herbrand originally proved his theorem for arbitrary formulas of first-order logic, [ 2 ] the simpler version shown here, restricted to formulas in prenex form ...