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Results tagged with lo.logic
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user 8246
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
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Natural number properties as uninterpreted functions in first order logic
Can we express the following property of natural numbers as FOL. The property given below is only indicative, I am more interested in knowing how the concepts such as "infinitely many X exists for so …
CommunityBot
- 1
0
votes
1
answer
236
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Models for the given FOL statement
Consider the following FOL sentence:
$\phi = \exists x \forall y \exists z ((x=y) \lor (P(x,y,z) \land \lnot P(y,x,z) ) $
It can be proven that for any natural number n > 0 there exits a model of si …
- 24.8k
2
votes
1
answer
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Graph properties and infinite FOL sentences
This question is related to this Question.
Above questions revealed that even though FOL is not expressive enough to describe properties such as Connectivity, Bipartite etc. It is possible to expres …
CommunityBot
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3
votes
2
answers
2k
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Graph properties and FOL
If a certain property of graphs cant not be expressed by a first order logic sentence $\phi$ over $\Sigma$ then can we say with confidence that such as property can not be expressed even by a an infin …
CommunityBot
- 1
1
vote
1
answer
624
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Exponent function as uninterpreted function in first order logic
I want to express the following sentence in first order logic.
There are naturals numbers that can not be expressed as one natural number raised to the power of another natural number other than one …
- 20.8k
5
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2
answers
2k
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Horn clauses and satisfiability
It is well known that satisfiability of Horn formulae can be checked in polynomial time using unit propagation.
But suppose we relax the condition for horn clauses from at most one un-negated literal …
- 44.4k