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A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]
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.
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.
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.
SPASS is a first-order logic theorem prover with equality. This is developed by the research group Automation of Logic, Max Planck Institute for Computer Science. The Theorem Prover Museum [27] is an initiative to conserve the sources of theorem prover systems for future analysis, since they are important cultural/scientific artefacts. It has ...
Horn clauses play a basic role in constructive logic and computational logic. They are important in automated theorem proving by first-order resolution , because the resolvent of two Horn clauses is itself a Horn clause, and the resolvent of a goal clause and a definite clause is a goal clause.
In predicate logic, universal instantiation [1] [2] [3] (UI; also called universal specification or universal elimination, [citation needed] and sometimes confused with dictum de omni) [citation needed] is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class.