FIRST-ORDER LOGIC

Copyright © Philip M. Parker, INSEAD. Terms of Use.

FIRST-ORDER LOGIC

Specialty Definition: FIRST-ORDER LOGIC

Domain	Definition
Computing	First-order logic The language describing the truth of mathematical formulas. Formulas describe properties of terms and have a truth value. The following are atomic formulas: True False p(t1,..tn) where t1,..,tn are terms and p is a predicate. If F1, F2 and F3 are formulas and v is a variable then the following are compound formulas: F1 ^ F2 conjunction - true if both F1 and F2 are true, F1 V F2 disjunction - true if either or both are true, F1 => F2 implication - true if F1 is false or F2 is true, F1 is the antecedent, F2 is the consequent (sometimes written with a thin arrow), F1 <= F2 true if F1 is true or F2 is false, F1 == F2 true if F1 and F2 are both true or both false (normally written with a three line equivalence symbol) ~F1 negation - true if f1 is false (normally written as a dash '-' with a shorter vertical line hanging from its right hand end). For all v . F universal quantification - true if F is true for all values of v (normally written with an inverted A). Exists v . F existential quantification - true if there exists some value of v for which F is true. (Normally written with a reversed E). The operators ^ V => <= == ~ are called connectives. "For all" and "Exists" are quantifiers whose scope is F. A term is a mathematical expression involving numbers, operators, functions and variables. The "order" of a logic specifies what entities "For all" and "Exists" may quantify over. First-order logic can only quantify over sets of atomic propositions. (E.g. For all p . p => p). Second-order logic can quantify over functions on propositions, and higher-order logic can quantify over any type of entity. The sets over which quantifiers operate are usually implicit but can be deduced from well-formedness constraints. In first-order logic quantifiers always range over ALL the elements of the domain of discourse. By contrast, second-order logic allows one to quantify over subsets of M. ["The Realm of First-Order Logic", Jon Barwise, Handbook of Mathematical Logic (Barwise, ed., North Holland, NYC, 1977)]. (1995-05-02). Source: The Free On-line Dictionary of Computing.
Source: compiled by the editor from various references; see credits.

Crosswords: FIRST-ORDER LOGIC

Specialty definitions using "FIRST-ORDER LOGIC": automated learning with a logical yoke ♦ deductive database ♦ equational logic. (references)

Source: compiled by the editor from various references; see credits.

Synonym: FIRST-ORDER LOGIC

Synonym by domain: first-order (language).

Commercial Usage: FIRST-ORDER LOGIC

Domain	Title
Books	A Philosophical Companion to First-Order Logic (reference) First-Order Logic (reference) The Language of First-Order Logic : Including the IBM-compatible Windows version of Tarski's World 4.0 (reference) (more book examples)
Source: compiled by the editor from various references; see credits.

Anagrams: FIRST-ORDER LOGIC

Scrabble® Enable2K-Verified Anagrams
	Words within the letters "c-d-e-f-g-i-i-l-o-o-r-r-r-s-t"
	-5 letters: clitorides, glorifiers, ideologist, tricolored.
Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.

Alternative Orthography: FIRST-ORDER LOGIC

Hexadecimal (or equivalents, 770AD-1900s) (references)

46 49 52 53 54 2D 4F 52 44 45 52 4C 4F 47 49 43

Leonardo da Vinci (1452-1519; backwards) (references)

Binary Code (1918-1938, probably earlier) (references)

01000110 01001001 01010010 01010011 01010100 00101101 01001111 01010010 01000100 01000101 01010010 00100000 01001100 01001111 01000111 01001001 01000011

HTML Code (1990) (references)

&#70 &#73 &#82 &#83 &#84 &#45 &#79 &#82 &#68 &#69 &#82 &#32 &#76 &#79 &#71 &#73 &#67

ISO 10646 (1991-1993) (references)

0046 0049 0052 0053 0054 002D 004F 0052 0044 0045 0052 004C 004F 0047 0049 0043

Encryption (beginner's substitution cypher): (references)

404352535415495238395224649414337

INDEX

1. Synonyms
2. Crosswords
3. Usage: Commercial
4. Anagrams

5. Orthography
6. Bibliography

Copyright © Philip M. Parker, INSEAD. Terms of Use.