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glossary

From: pat hayes <phayes@ai.uwf.edu>
Date: Tue, 3 Dec 2002 13:27:07 -0600
Message-Id: <p05111b11ba12aeaf4155@[10.0.100.247]>
To: w3c-rdfcore-wg@w3.org

Guys, after recent email feedback about the incomprehensibility of 
the MT for non-math readers, I thought it might be helpful to include 
a glossary as an appendix. Since it might be useful more generally, 
here it is in current draft form. To track it, use
http://www.coginst.uwf.edu/~phayes/Glossary-RDF-draft.html

Feel free to add to it or suggest modifications/additions.

Pat
--------------
Glossary of technical terms

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

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

Class (n.) A general concept, category or classification. Any 
resource used primarily to classify or categorize other resources. 
Formally, a resource of type rdfs:Class with an associated set of 
resources all of which are said to have the class as their rdf:type. 
Classes are often called 'predicates' in the formal logical 
literature.

Complete (adj., of an inference system). Able to draw all valid 
inferences. See Inference. Also used with a qualifier: able to 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.)

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

Correct (adj., of an inference system). Unable to draw any invalid 
inferences. See Inference.

Entailment (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.)

Extensional (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.

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

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

Infer (v.t.) To draw the conclusion ... , to perform an inference 
resulting in ... .

Inference (n.) Any process which constructs new expressions from 
existing expressions, or which delivers an answer to a query of the 
form 'do these expressions entail that expression?'. Inferences 
corresponding to entailments are described as correct or valid.

Inference system (n., also Inference engine.) Any implemented system 
for performing inference. Often defined in terms of a set of rules 
together with a strategy for applying them.

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

(The merits and demerits of intensionality have been extensively 
debated in the philosophical logic literature. Extensional semantic 
theories are simpler, and conventional semantics for formal logics 
usually assume an extensional view, but conceptual analysis of 
ordinary language often suggests that intensional thinking is more 
natural. Examples often cited are that an extensional logic is 
obliged to treat all 'empty' extensions as identical, so must 
identify 'round square' with 'santa clause', and is unable to 
distinguish concepts that 'accidentally' have the same instances, 
such as human beings and hairless bipedal hominids. RDF model theory 
is basically intensional but has some extensional aspects, most 
notably in the 'if and only if' conditions in the definitions of 
rdfs:subClassOf and rdfs:subPropertyOf, which force these properties 
to take account only of the class and property extensions.)

Interpretation (of) (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.

(Some logic texts distinguish between a interpretation structure, 
which is a 'possible world' considered as something independent of 
any particular vocabulary, and an interpretation mapping from a 
vocabulary into the structure. The RDF semantics takes the simpler 
route of merging these into a single concept.)

Logic (n.) A formal language which expresses propositions.

Monotonic (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 suppositions cannot invalidate a valid entailment.

(All logics based on a conventional model theory and a standard 
notion of entailment are monotonic. Monotonic logics have the 
property that entailments can be taken as valid outside of the 
context in which they were generated. This is why RDF is designed to 
be monotonic.)

Nonmonotonic (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 (eg birds usually 
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 hse is not an employee.)

(The relationship between monotonic and nonmonotonic inferences is 
often subtle. For example, if a closed-world assumption is made 
explicit, e.g. by asserting explicitly that the corpus is complete 
and providing explicit provenance information in the conclusion, then 
closed-world reasoning is monotonic; it is the implicitness that 
makes the reasoning nonmonotonic. Nonmonotonic conclusions can be 
said to be valid only in some kind of 'context', and are liable to be 
incorrect or misleading when used outside that context. Making the 
context explicit in the reasoning and visible in the conclusion is a 
way to map them into a monotonic framework.)

Proposition (n.) Something that has a truth-value.

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

Satisfy (v.t.), satisfaction,(n.) satisfying (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.

Universe (n., also Universe of discourse) The universal 
classification, or the set of all things that an interpretation 
considers to exist.

Valid (adj., of an inference) Corresponding to an entailment, i.e. 
the conclusion of the inference is entailed by the antecedent of the 
inference.

Well-formed (adj., of an expression). Syntactically legal.

World (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.

(The exact metaphysical status of 'possible worlds' is highly 
controversial. Fortunately, one does not need to committ oneself to a 
belief in parallel universes in order to use the concept in its 
second and third senses, which are sufficient for semantic purposes.)


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Received on Tuesday, 3 December 2002 14:26:46 EST

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