# 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

Fragment (logic), a syntactically restricted subset of a logical language

### 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.