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Oxford: Oxford University Press.189van Benthem, J. (1983). The logic of time. Dordrecht, Holland: D. Reidel Pub. Co.Zachman, J. (1986). A framework for information systems architecture. IBM Systems Journal,26(3), 276-292.190APPENDIX A: IDEF3 ELABORATION LANGUAGEThis appendix contains a detailed description of the IDEF3 elaboration language including aBackus-Naur form (BNF) specification. The IDEF3 elaboration language is broken into twoparts: a core language that defines that basic syntactic apparatus and associated logical axiomsneeded in almost any logical language, and an extension of the core language that includesadditional syntactic apparatus, definitions that introduce specialized terms for talking aboutsituations, UOBs and other IDEF3 specific entities, and axioms that constrain their basic use.The core language is loosely based on the Knowledge Interchange Format (KIF) (Genesereth &Fikes, 1992), though a number of constructs—set theoretic ones, in particular—are omitted.
InSection A.1, each syntactic category of the core is discussed and examples are given to illustratehow elements of the category are used. A formal BNF is then specified in Section A.2, and anumber of definitions and concomitant axioms are provided. An overview of situation theory isprovided in Section A.4 to motivate the IDEF3-specific extensions that are introduced. The basicbehavior of these extensions is then axiomatized with commentary in Section A.5.A.1A.1.1Description of the Elaboration Language CoreBasic Syntactic TypesThe basic syntactic types of the elaboration language core are quite standard. They includethe following:•Letter: Letters are the upper and lower case letters of the alphabet.•Digits: The numerals 0 to 9.
Positive digits are the digits from 1 to 9.•Identifier: An identifier is any string of letters, digits, dashes, andunderscores that begins with a letter and ends with a letter or digit.•Punctuation: Punctuation consists of the ASCII characters that are neitherletters nor digits.•Polarity: A polarity is either the plus sign “+” or the minus sign “–”. Theseplay a special role in terms denoting infons.•Posint: A posint is any sequence of digits of length greater than 0, i.e.,intuitively, any numeral that denotes a positive integer. It must begin with apositive digit unless it is simply the digit 0.•Unsigned int: An unsigned int is the digit 0 or a posint.•Int: An int is either an unsigned digit or a minus sign “–” followed by aposint.193A.1.2•Exponents: An exponent is the letter “E” or “e” followed by an int.•Float: A float is either an int followed by an exponent, or an optional plusor minus sign followed by an int followed by a decimal point followed by astring of digits followed by an exponent.•Number: A number is either an integer or a floating point.•String: A string is any sequence of ASCII characters (including whitespace) preceded by and ending with the double quote character “"”.•Variable: A variable is any identifier preceded by a question mark “?”.The variables of the core IDEF3 elaboration language are completelyuntyped; no distinction is made even between relation variables andindividual variables, a distinction that is drawn in most logical languages.Rather, typing is enforced by means of IDEF3 specific axioms anddefinitions that introduce the basic semantical categories of the intendedsemantics language and characterize their properties and the relationsbetween them; see Section A.3.OperatorsOperators are reserved expressions used to form more complex expressions, specifically,terms, sentences, and definitions.
The operators that are part of the IDEF3 Elaboration Languageare presented in this subsection.•Definition Operators: These operators are used to form definitions foridentifiers that are intended to denote an object in one of the basic semanticcategories of the language: define-individual, define-function, and definerelation.•Term Operators: These operators are used to form complex terms.
Thereare six such operators: listof, the, number-of, if, cond, lambda, andkappa.•Sentence Operators: These operators are used to form complex sentences.The IDEF3 Elaboration Language includes common Boolean and relatedtruth functional operators (not, and, or, xor (exclusive disjunction), =>(implication), and <=> (co-implication). It also includes the standarduniversal and existential quantifiers forall and exists, as well as an array ofnumerical existential quantifiers exists-1 (there exists at least one—equivalent simply to exists) exists!-1 (there exists exactly one), exists-2(there exist at least 2), exists!-2 (there exist exactly two), and so on.194A.1.3TermsThe IDEF3 Elaboration Language supports three types of expressions: terms, sentences, anddefinitions.
A term denotes an object of some sort, though exactly what sort is not determined bythe language itself (unlike highly typed languages) but rather separately by means of specialaxioms (as illustrated below). Terms are divided into the following categories:•Atomic Terms: This category includes all the central simple types of thelanguage, viz., identifiers, variables, ints, floats, and strings.•Complex Terms: A complex term is a term that is built up, ultimately fromsimpler terms and (perhaps) a sentence and/or operator.
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