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

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.) -- --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32501 (850)291 0667 cell phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes s.pam@ai.uwf.edu for spamReceived on Tuesday, 3 December 2002 14:26:46 EST

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