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Kaveh
Kaveh
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I an not sure what you are looking for exactly. Note that $\sup$ and $\inf$ are included as operators in the language so any Skolemization would need to have them.

BenyacovBenYaacov et al. give some quantifier elimination results for continuous logic theories in the following paper:

Here is an alternative view that I personally find easier to work with and might be helpful:

theories in continuous logic can be thought of as theories in first-order rational Pavelka logic $RPL\forall$, which is in turn a conservative extension of classical first-order logic.

We use this to construct Henkin models for CL in the following paper:

The reference to learn more about $RPL\forall$ is

You may want to also check:

  • Chang and Keisler, "Continuous Model Theory", 1966.
  • Metcalfe, Olivetti, and Gabbay, "Proof Theory for Fuzzy Logics", 2009.

I an not sure what you are looking for exactly. Note that $\sup$ and $\inf$ are included as operators in the language so any Skolemization would need to have them.

Benyacov et al. give some quantifier elimination results for continuous logic theories in the following paper:

Here is an alternative view that I personally find easier to work with and might be helpful:

theories in continuous logic can be thought of as theories in first-order rational Pavelka logic $RPL\forall$, which is in turn a conservative extension of classical first-order logic.

We use this to construct Henkin models for CL in the following paper:

The reference to learn more about $RPL\forall$ is

You may want to also check:

  • Chang and Keisler, "Continuous Model Theory", 1966.
  • Metcalfe, Olivetti, and Gabbay, "Proof Theory for Fuzzy Logics", 2009.

I an not sure what you are looking for exactly. Note that $\sup$ and $\inf$ are included as operators in the language so any Skolemization would need to have them.

BenYaacov et al. give some quantifier elimination results for continuous logic theories in the following paper:

Here is an alternative view that I personally find easier to work with and might be helpful:

theories in continuous logic can be thought of as theories in first-order rational Pavelka logic $RPL\forall$, which is in turn a conservative extension of classical first-order logic.

We use this to construct Henkin models for CL in the following paper:

The reference to learn more about $RPL\forall$ is

You may want to also check:

  • Chang and Keisler, "Continuous Model Theory", 1966.
  • Metcalfe, Olivetti, and Gabbay, "Proof Theory for Fuzzy Logics", 2009.
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Kaveh
Kaveh
  • 5.5k
  • 2
  • 37
  • 52

I an not sure what you are looking for exactly. Note that $\sup$ and $\inf$ are included as operators in the language so any Skolemization would need to have them.

Benyacov et al. give some quantifier elimination results for continuous logic theories in the following paper:

Here is an alternative view that I personally find easier to work with and might be helpful:

theories in continuous logic can be thought of as theories in first-order rational Pavelka logic $RPL\forall$, which is in turn a conservative extension of classical first-order logic.

We use this to construct Henkin models for CL in the following paper:

The reference to learn more about $RPL\forall$ is

You may want to also check:

  • Chang and Keisler, "Continuous Model Theory", 1966.
  • Metcalfe, Olivetti, and Gabbay, "Proof Theory for Fuzzy Logics", 2009.