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...
32 KB (4,399 words) - 12:11, 1 July 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
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy...
93 KB (13,105 words) - 19:44, 16 August 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
A second-order propositional logic is a propositional logic extended with quantification over propositions. A special case are the logics that allow second-order...
1 KB (121 words) - 10:38, 8 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...
111 KB (11,052 words) - 11:45, 6 August 2024
Consistency (redirect from Consistency (Mathematical Logic))
(1924), von Neumann (1927) and Herbrand (1931). Stronger logics, such as second-order logic, are not complete. A consistency proof is a mathematical proof...
20 KB (2,914 words) - 02:18, 23 July 2024
first-order logic, the most important case, it follows from the completeness theorem that the two meanings coincide. In other logics, such as second-order logic...
13 KB (1,686 words) - 17:06, 22 April 2023
of logics in contrast to one universally true logic. These logics can be divided into classical logic, usually identified with first-order logic, extended...
97 KB (11,673 words) - 16:51, 21 August 2024
derivative is the second Second-order logic, an extension of predicate logic Second-order perturbation, in perturbation theory Second-order cybernetics, the...
1 KB (198 words) - 17:14, 12 December 2022
In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative...
29 KB (3,848 words) - 11:45, 23 August 2024
languages expressible by sentences of existential second-order logic; that is, second-order logic excluding universal quantification over relations,...
18 KB (2,543 words) - 22:33, 28 July 2024
within second order logic or higher order logics. Quantifiers have been generalized beginning with the work of Mostowski and Lindström. In a first-order logic...
31 KB (4,537 words) - 17:47, 1 May 2024
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical...
154 KB (16,846 words) - 15:13, 24 August 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 (8,331 words) - 12:56, 25 July 2024
Zorn's lemma.) In second-order logic, however, the well-ordering theorem is strictly stronger than the axiom of choice: from the well-ordering theorem one may...
7 KB (989 words) - 17:35, 14 March 2024
In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional...
16 KB (1,901 words) - 20:59, 8 May 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) - 15:25, 3 July 2024
in first-order logic. But they can be expressed in second-order logic with only a few axioms. But despite this advantage, first-order logic is still much...
59 KB (7,022 words) - 17:02, 14 May 2024
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 (10,723 words) - 18:49, 8 May 2024
languages are precisely the ones definable in a particular monadic second-order logic called S1S. Wolfgang Thomas, "Automata on infinite objects." In Jan...
5 KB (603 words) - 16:59, 3 August 2022
is the set of languages expressible in existential second-order logic—that is, second-order logic restricted to exclude universal quantification over...
63 KB (7,780 words) - 18:30, 24 August 2024
mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some...
76 KB (11,833 words) - 16:17, 18 July 2024
Löwenheim–Skolem theorem (category Mathematical logic)
characterize first-order logic. In general, the Löwenheim–Skolem theorem does not hold in stronger logics such as second-order logic. In its general form...
22 KB (2,795 words) - 06:31, 25 July 2024
(graph theory) In logic, model theory and type theory: Zeroth-order logic First-order logic Second-order logic Higher-order logic Order (journal), an academic...
4 KB (501 words) - 09:50, 19 February 2023
theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem...
17 KB (2,329 words) - 09:36, 10 June 2024
Natural deduction (redirect from Natural deduction logic)
work on natural deduction, and included applications for modal and second-order logic. In natural deduction, a proposition is deduced from a collection...
68 KB (6,768 words) - 05:11, 5 July 2024
Dependence logic is a logical formalism, created by Jouko Väänänen, which adds dependence atoms to the language of first-order logic. A dependence atom...
28 KB (4,500 words) - 13:41, 28 February 2024
Satisfiability (redirect from Satisfiability (logics))
respect to a fixed logic defining the syntax of allowed symbols, such as first-order logic, second-order logic or propositional logic. Rather than being...
12 KB (1,500 words) - 18:45, 26 November 2022
first-order logic of graphs concerns sentences in which the variables and predicates concern individual vertices and edges of a graph, while monadic second-order...
39 KB (4,985 words) - 01:40, 7 November 2023