Fragment (logic)

fragmentfragments
In mathematical logic, a fragment of a logical language or theory is a subset of this logical language obtained by imposing syntactical restrictions on the language.wikipedia
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Mathematical logic

formal logicsymbolic logiclogic
In mathematical logic, a fragment of a logical language or theory is a subset of this logical language obtained by imposing syntactical restrictions on the language.

Theory (mathematical logic)

theorytheoriesformal theories
In mathematical logic, a fragment of a logical language or theory is a subset of this logical language obtained by imposing syntactical restrictions on the language.

Syntax

syntacticsyntacticalsyntactically
In mathematical logic, a fragment of a logical language or theory is a subset of this logical language obtained by imposing syntactical restrictions on the language.

Well-formed formula

formulaformulaswell-formed
Hence, the well-formed formulae of the fragment are a subset of those in the original logic.

Computational complexity theory

computational complexitycomplexity theorycomplexity
The computational complexity of tasks such as satisfiability or model checking for the logical fragment can be no higher than the same tasks in the original logic, as there is a reduction from the first problem to the other. The field of descriptive complexity theory aims at establishing a link between logics and computational complexity theory, by identifying logical fragments that exactly capture certain complexity classes.

Satisfiability

satisfiablesatisfiability problemsatisfies
The computational complexity of tasks such as satisfiability or model checking for the logical fragment can be no higher than the same tasks in the original logic, as there is a reduction from the first problem to the other.

Model checking

model checkermodel checkerssymbolic model checking
The computational complexity of tasks such as satisfiability or model checking for the logical fragment can be no higher than the same tasks in the original logic, as there is a reduction from the first problem to the other.

Reduction (complexity)

reductionreducedreductions
The computational complexity of tasks such as satisfiability or model checking for the logical fragment can be no higher than the same tasks in the original logic, as there is a reduction from the first problem to the other.

Computational logic

logic and computationprogramming logics
An important problem in computational logic is to determine fragments of well-known logics such as first-order logic that are as expressive as possible yet are decidable or more strongly have low computational complexity.

First-order logic

predicate logicfirst-orderpredicate calculus
An important problem in computational logic is to determine fragments of well-known logics such as first-order logic that are as expressive as possible yet are decidable or more strongly have low computational complexity.

Descriptive complexity theory

descriptive complexitydescriptional complexitylogical characterization
The field of descriptive complexity theory aims at establishing a link between logics and computational complexity theory, by identifying logical fragments that exactly capture certain complexity classes.

Complexity class

complexity classescomputational complexityclasses
The field of descriptive complexity theory aims at establishing a link between logics and computational complexity theory, by identifying logical fragments that exactly capture certain complexity classes.

Two-variable logic

two-variable logic with counting
In mathematical logic and computer science, two-variable logic is the fragment of first-order logic where formulae can be written using only two different variables.

Monadic second-order logic

monadic second-ordermonadic second order logicmonadic second order theory
However, MSO is the fragment in which second-order quantification is limited to monadic predicates (predicates having a single argument).

Abstract elementary class

Abstract Elementary ClassesAECs
If \phi is a sentence in the infinitary logic, and \mathcal{F} is a countable fragment containing \phi, then is an AEC with Löwenheim–Skolem number \aleph_0. This can be generalized to other logics, like, or, where Q expresses "there exists uncountably many".

Description logic

description logicsAttributive concept Language with ComplementsDescription Logic Modeling
Many DLs are decidable fragments of first-order logic (FOL) and are usually fragments of two-variable logic or guarded logic.

Fragment

Logic of graphs

However, connectivity cannot be expressed in first-order graph logic, nor can it be expressed in existential MSO 1 (the fragment of MSO 1 in which all set quantifiers are existential and occur at the beginning of the sentence) nor even existential MSO 2.

Red Star OS

Red StarRed Star operating system
This is probably due to a problem when processing URLs that perform functions such as Mailto or calendar without the parameters to clean up unwanted code fragments.