Translation of infinite-valued QBF to first order logic

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Quantified Boolean Formulas with infinite values are distinct from their usual 2-valued version (proof).



Is there a known way to express such formulas in standard first order logic notation (so that they can be fed to a first order logic theorem prover? What I have in mind is some scheme similar to how modal logics (with infinite number of truth values) can be simulated using the so-called Standard Translation into first order logic. Obviously, a direct translation using a single-argument truth predicate assumes two values and is not applicable in this case, the truth predicate involved probably needs two arguments, as in the Standard Translation. I apologize beforehand for the exploratory nature of the question.




logic first-order-logic quantifiers




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  • This paper on the decision problem for boolean algebras may be of interest.
    – Rob Arthan
    Jul 31 at 22:11














up vote
2
down vote

favorite












Quantified Boolean Formulas with infinite values are distinct from their usual 2-valued version (proof).



Is there a known way to express such formulas in standard first order logic notation (so that they can be fed to a first order logic theorem prover? What I have in mind is some scheme similar to how modal logics (with infinite number of truth values) can be simulated using the so-called Standard Translation into first order logic. Obviously, a direct translation using a single-argument truth predicate assumes two values and is not applicable in this case, the truth predicate involved probably needs two arguments, as in the Standard Translation. I apologize beforehand for the exploratory nature of the question.




logic first-order-logic quantifiers




share|cite|improve this question



















  • This paper on the decision problem for boolean algebras may be of interest.
    – Rob Arthan
    Jul 31 at 22:11












up vote
2
down vote

favorite









up vote
2
down vote

favorite











Quantified Boolean Formulas with infinite values are distinct from their usual 2-valued version (proof).



Is there a known way to express such formulas in standard first order logic notation (so that they can be fed to a first order logic theorem prover? What I have in mind is some scheme similar to how modal logics (with infinite number of truth values) can be simulated using the so-called Standard Translation into first order logic. Obviously, a direct translation using a single-argument truth predicate assumes two values and is not applicable in this case, the truth predicate involved probably needs two arguments, as in the Standard Translation. I apologize beforehand for the exploratory nature of the question.




logic first-order-logic quantifiers




share|cite|improve this question











Quantified Boolean Formulas with infinite values are distinct from their usual 2-valued version (proof).



Is there a known way to express such formulas in standard first order logic notation (so that they can be fed to a first order logic theorem prover? What I have in mind is some scheme similar to how modal logics (with infinite number of truth values) can be simulated using the so-called Standard Translation into first order logic. Obviously, a direct translation using a single-argument truth predicate assumes two values and is not applicable in this case, the truth predicate involved probably needs two arguments, as in the Standard Translation. I apologize beforehand for the exploratory nature of the question.





logic first-order-logic quantifiers





share|cite|improve this question










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asked Jul 31 at 11:44









Akuri

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  • This paper on the decision problem for boolean algebras may be of interest.
    – Rob Arthan
    Jul 31 at 22:11
















  • This paper on the decision problem for boolean algebras may be of interest.
    – Rob Arthan
    Jul 31 at 22:11















This paper on the decision problem for boolean algebras may be of interest.
– Rob Arthan
Jul 31 at 22:11




This paper on the decision problem for boolean algebras may be of interest.
– Rob Arthan
Jul 31 at 22:11















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