(n.) In an inference, the
expression(s) from which the conclusion is derived. In an entailment relation, the
entailer. Also *assumption*.

(n.) (i) Any expression which is claimed to be true. (ii) The act of claiming something to be true.

(n.) A general concept, category or classification. Something used primarily to
classify or categorize other things. Formally, in RDF, a resource of type
`rdfs:Class`

with an associated set of resources all of which
have the class as a value of the `rdf:type`

property.
Classes are often called 'predicates' in the formal logical
literature.

(adj., of an inference system). (1)
Able to detect all entailments between any two expressions.
(2) Able to draw all valid inferences. See *Inference*. Also used with a qualifier: able to
detect entailments or draw all valid inferences in a certain limited form or kind (e.g.
between expressions in a certain normal form, or meeting certain syntactic conditions.)

(n.) In an inference,
the expression constructed from the antecedent. In an entailment relation, the
entailee. Also *conclusion*.

(adj., of an expression) Having
a satisfying interpretation; not internally contradictory. (Also used
of an inference system as synonym for *Correct*.)

(adj., of an inference system). Unable
to draw any invalid inferences, or unable to make false claims of entailment. See *Inference*.

(adj., of an inference system). Able to determine for any pair of expressions, in a finite time with finite resources, whether or not the first entails the second. (Also: adj., of a logic:) Having a decideable inference system which is complete and correct for the semantics of the logic.

(v.), (n.). A semantic relationship between expressions which holds whenever the truth of the first guarantees the truth of the second. Equivalently, whenever it is logically impossible for the first expression to be true and the second one false. Equivalently, when any interpretation which satisfies the first also satisfies the second. (Also used between a set of expressions and an expression.)

(prep., with
*to*) True under exactly the same conditions; making
identical claims about the world, when asserted. Entails and is entailed
by.

(adj., of a logic) A
set-based theory or logic of classes, in which classes are
considered to be sets, properties considered to be sets of
<object, value> pairs, and so on. A theory which admits no
distinction between entities with the same extension. See *Intensional*.

(adj.) Couched in language sufficiently precise as to enable results to be established using conventional mathematical techniques.

(conj.) Conventional abbreviation for 'if and only if'. Used to express necessary and sufficient conditions.

(adj.) False under all interpretations; impossible to satisfy. (n.), any inconsistent expression or graph.

(adj., of an expression) having a meaning which implicitly refers to the context of use. Examples from English include words like 'here', 'now', 'this'.

(n.) An act or
process of constructing new expressions from existing expressions, or the result
of such an act or process. Inferences corresponding to entailments are described as *correct* or *valid*.
, formal description of a type of inference;
, organized system of inference rules; also,
software which generates inferences or checks inferences for validity.

(adj., of a logic) Not extensional. A logic which allows distinct entities with the same extension.

() (n.) A minimal formal description of those aspects of a world which is just sufficient to establish the truth or falsity of any expression of a logic.

(n.) A formal language which expresses propositions.

(adj.). Concerned with the true nature of things in some absolute or fundamental sense.

(n.) A formal semantic theory which relates expressions to interpretations.

(adj., of a logic or inference system) Satisfying the condition that if S entails E then (S + T) entails E, i.e. adding information to some antecedents cannot invalidate a valid entailment.

(adj.,of a logic
or inference system) Not monotonic. Non-monotonic formalisms have been
proposed and used in AI and various applications. Examples of
nonmonotonic inferences include *default reasoning*, where
one assumes a 'normal' general truth unless it is contradicted by
more particular information (birds normally fly, but penguins
don't fly); *negation-by-failure*, commonly assumed in logic
programming systems, where one concludes, from a failure to prove a
proposition, that the proposition is false; and *implicit
closed-world assumptions*, often assumed in database
applications, where one concludes from a lack of information about
an entity in some corpus that the information is false (e.g. that
if someone is not listed in an employee database, that he or she is not
an employee.)

(adj.) (Philosophy) Concerned with what kinds of things really exist. (Applied) Concerned with the details of a formal description of some topic or domain.

(n.) Something that has a truth-value; a statement or expression that is true or false.

(v.), (n.) To categorize as an object; to describe as an entity. Often used to describe a convention whereby a syntactic expression is treated as a semantic object and itself described using another syntax. In RDF, a reified triple is a description of a triple-token using other RDF triples.

(n.)(as used in RDF)(i) An entity; anything in the universe. (ii) As a class name: the class of everything; the most inclusive category possible.

(v.t.), ,(n.) (adj., of an interpretation). To make true. The basic semantic relationship between an interpretation and an expression. X satisfies Y means that if the world conforms to the conditions described by X, then Y must be true.

(adj.) ,
(n.). Concerned with the specification
of meanings. Often contrasted with *syntactic* to emphasize
the distinction between expressions and what they denote.

(n., also *Universe of
discourse*) The universal classification, or the set of all
things that an interpretation considers to exist. In RDF/S, this is
identical to the set of resources.

(v.)
contrasted with *mention*; to use a piece of syntax to
denote or refer to something else. The normal way that language is
used.

(adj., of an inference or inference process) Corresponding to an entailment, i.e. the
conclusion of the inference is entailed by the antecedent of the
inference. Also *correct*.

(n.) (with *the:*) (i) The actual world. (with
*a:*) (ii) A way that the actual world might be arranged.
(iii) An interpretation (iv) A possible world.