First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics... 93 KB (13,173 words) - 20:30, 24 April 2024 |
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic... 31 KB (4,321 words) - 11:40, 19 February 2024 |
In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers... 9 KB (1,061 words) - 10:50, 5 December 2023 |
Propositional calculus (redirect from Zeroth order logic) branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals... 138 KB (15,652 words) - 09:41, 28 April 2024 |
self-reference", as in first-order logic and other logic uses, where it is contrasted with "allowing some self-reference" (higher-order logic) In detail, it may... 3 KB (376 words) - 10:47, 2 May 2020 |
between "tautology" and "logically valid" in the context of first-order logic . Propositional logic begins with propositional variables, atomic units that... 21 KB (2,970 words) - 09:11, 29 March 2024 |
and first-order logic. The sentences that are made true by a particular assignment are said to be satisfied by that assignment. In classical logic, no... 32 KB (4,421 words) - 20:08, 14 February 2024 |
Extensions of First Order Logic is a book on mathematical logic. It was written by María Manzano, and published in 1996 by the Cambridge University Press... 5 KB (591 words) - 14:36, 11 December 2021 |
contains logic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of logic symbols. In logic, a set... 26 KB (304 words) - 17:37, 26 April 2024 |
the translation of the English sentence "some men are bald" into first-order logic as ∃x(M(x)∧B(x)){\displaystyle \exists x(M(x)\land B(x))}. The purpose... 63 KB (7,510 words) - 13:50, 28 February 2024 |
classical logics such as second-order logic or infinitary logic are also studied, along with Non-classical logics such as intuitionistic logic. First-order logic... 68 KB (8,329 words) - 22:09, 28 April 2024 |
mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood... 13 KB (1,686 words) - 17:06, 22 April 2023 |
Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical... 84 KB (10,717 words) - 06:55, 26 April 2024 |
In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model... 14 KB (1,948 words) - 18:48, 19 January 2024 |
of logics in contrast to one universally true logic. These logics can be divided into classical logic, usually identified with first-order logic, extended... 96 KB (11,673 words) - 08:57, 15 April 2024 |
In logic, a predicate is a symbol that represents a property or a relation. For instance, in the first-order formula P(a){\displaystyle P(a)}, the symbol... 4 KB (416 words) - 16:12, 26 February 2024 |
theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts... 28 KB (4,066 words) - 04:41, 15 February 2024 |
answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. Logical systems are decidable if membership... 16 KB (1,901 words) - 00:38, 9 January 2024 |
second order logic or higher order logics. Quantifiers have been generalized beginning with the work of Mostowski and Lindström. In a first-order logic statement... 31 KB (4,529 words) - 07:28, 30 April 2024 |
Common Logic (CL) is a framework for a family of logic languages, based on first-order logic, intended to facilitate the exchange and transmission of... 4 KB (456 words) - 04:48, 4 February 2024 |
view, structures are the objects used to define the semantics of first-order logic, cf. also Tarski's theory of truth or Tarskian semantics. For a given... 34 KB (5,097 words) - 17:45, 30 March 2024 |
Consistency (redirect from Consistency (Mathematical Logic)) specified formal system). A set of formulas Φ {\displaystyle \Phi } in first-order logic is consistent (written Con Φ {\displaystyle \operatorname {Con}... 19 KB (2,791 words) - 17:55, 26 February 2024 |
In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of... 20 KB (2,807 words) - 15:57, 3 December 2023 |
In first-order logic, a first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model... 36 KB (5,269 words) - 04:45, 30 April 2024 |
In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification... 11 KB (1,308 words) - 06:51, 8 August 2023 |
specifically propositional and first-order logic, as opposed to the other forms of classical logic. Most semantics of classical logic are bivalent, meaning all... 6 KB (763 words) - 23:22, 7 April 2024 |
described first-order logic (FOL) as the metric by which all AI knowledge representation formalisms should be evaluated. First-order logic is a general... 16 KB (1,721 words) - 13:02, 19 January 2024 |
more expressive than propositional logic but less expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are... 38 KB (4,209 words) - 15:08, 23 April 2024 |