Search results
Results From The WOW.Com Content Network
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.
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]
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 ...
The resultant predicate (λx.Q(x)) is a monadic predicate capable of taking a term t as argument as in (λx.Q(x))(t), which says that the object denoted by 't' has the property of being such that Q. The law of abstraction states ( λx.Q(x) )(t) ≡ Q(t/x) where Q(t/x) is the result of replacing all free occurrences of x in Q by t.
A further example, the description logic is the logic plus extended cardinality restrictions, and transitive and inverse roles. The naming conventions aren't purely systematic so that the logic A L C O I N {\displaystyle {\mathcal {ALCOIN}}} might be referred to as A L C N I O {\displaystyle {\mathcal {ALCNIO}}} and other abbreviations are also ...
When using reified fluents, a separate predicate is necessary to tell when a fluent is actually true or not. For example, H o l d s A t ( o n ( b o x , t a b l e ) , t ) {\displaystyle HoldsAt(on(box,table),t)} means that the box is actually on the table at time t {\displaystyle t} , where the predicate H o l d s A t {\displaystyle HoldsAt} is ...