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Re: glossary

From: Jos De_Roo <jos.deroo.jd@belgium.agfa.com>
Date: Wed, 4 Dec 2002 01:18:56 +0100
To: "pat hayes <phayes" <phayes@ai.uwf.edu>
Cc: w3c-rdfcore-wg@w3.org, w3c-rdfcore-wg-request@w3.org
Message-ID: <OF217F73D8.6404575A-ONC1256C85.0000CF6A-C1256C85.0001BBB8@agfa.be>

Pat, your glossary is simply the best

??? should it say something about use/mention
something a la

  whenever, in a sentence, we wish to say something
  about a certain thing, we have to use, in this
  sentence, not the thing itself but its name or
  designation -- Alfred Tarski

and all those "certain things" are rdf resources, wether
they be URI referenced things or (typed) literal values,
the names are just different designations

-- ,
Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/

                    pat hayes                                                                                           
                    <phayes@ai.uwf.edu>       To:     w3c-rdfcore-wg@w3.org                                             
                    Sent by:                  cc:                                                                       
                    w3c-rdfcore-wg-requ       Subject:     glossary                                                     
                    2002-12-03 08:27 PM                                                                                 

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

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

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

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

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

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

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

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 19:19:36 EST

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