Examples of 'second-order logic' in a sentence
Meaning of "second-order logic"
second-order logic - a type of mathematical logic that extends first-order logic by quantifying variables over sets rather than individual elements. This phrase is used in philosophy, mathematics, and computer science
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- A formal system which extends first-order logic by allowing quantification over relations between members of the universe.
How to use "second-order logic" in a sentence
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second-order logic
Second-order logic allows quantification over predicates.
Each logic we consider is a fragment of monadic second-order logic.
The syntax of second-order logic tells which expressions are well formed formulas.
We show that it is equivalent to monadic second-order logic on graphs.
Second-order logic extends first-order logic by adding the latter type of quantification.
Up to a certain notion of isomorphism, the powerset operation is definable in second-order logic.
When transitive closure is added to second-order logic instead, we obtain PSPACE.
There are also characterizations based on an equivalent form of automata and monadic second-order logic.
Second-order logic with Henkin semantics is not more expressive than first-order logic.
Systems of partially ordered quantification are intermediate in strength between first-order logic and second-order logic.
Monadic second-order logic.
Other higher-order logics allow quantification over even higher types than second-order logic permits.
Second-order logic is more expressive than first-order logic.
HP can be stated formally in systems of second-order logic.
Second-order logic is in turn extended by higher-order logic and type theory.
See also
PH has a simple logical characterization, it is the set of languages expressible by second-order logic.
It is controversial whether second-order logic with standard semantics is really " logic " at all.
This logic turns out to be equi-interpretable with monadic second-order logic.
Second-order logic and other higher-order logics are formal extensions of first-order logic.
The fragment of formula 8 formulas is defined dually, it is called universal second-order logic.
Logical systems extending first-order logic, such as second-order logic and type theory, are also undecidable.
In general, the Löwenheim-Skolem theorem does not hold in stronger logics such as second-order logic.
Just as in first-order logic, second-order logic may include non-logical symbols in a particular second-order language.
The languages in the polynomial hierarchy, PH, correspond to all of second-order logic.
Second-order logic - monadic version and Henkin semantics.
Arithmetic is then derivable in second-order logic from Hume 's principle.
Of second-order logic.
Linear temporal logic ( LTL ) is a fragment of S1S monadic second-order logic of one successor.
Existential second-order logic yields NP.
To this end, Takeuti 's conjecture speculates that a sequent formalisation of second-order logic has cut-elimination.
Semantics = = The semantics of second-order logic establish the meaning of each sentence.
Syntax and fragments = = The syntax of second-order logic tells which expressions are well formed formulas.
Frege 's logic, now known as second-order logic, can be weakened to so-called predicative second-order logic.
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Examples of using Second-order
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Second-order lines in the projective plane
Extendibility is a second-order analog of strong compactness
Second-order partial derivative differential equations
Examples of using Logic
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His cynical logic betrays a sick mind
Logic offers a serenity humans seldom experience
There is a certain logic behind such ideas
