Kripke semantics for higher-order type theory applied to constraint logic programming languages

Lipton, James; Nieva, Susana

doi:10.1016/j.tcs.2017.11.005

Cited by 2 publications

(2 citation statements)

References 43 publications

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“…However, as LDL is a richer language, we may no longer rely on this method. For a typed FOL, one could define a Kripke-style semantics [35,26] for characterising the set of all true formulae, or take provable FOL formulae to characterise the set of true FOL formulae. We take the latter approach.…”

Section: Soundness and Completeness Of Dlsmentioning

confidence: 99%

Logic of Differentiable Logics: Towards a Uniform Semantics of DL

Ślusarz¹,

Komendantskaya²,

Daggitt³

et al. 2023

Preprint

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Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates expressions in the syntax into loss functions. These loss functions can then be used during training with standard gradient descent algorithms. The variety of existing DLs and the differing levels of formality with which they are treated makes a systematic comparative study of their properties and implementations difficult. This paper remedies this problem by suggesting a meta-language for defining DLs that we call the Logic of Differentiable Logics, or LDL. Syntactically, it generalises the syntax of existing DLs to FOL, and for the first time introduces the formalism for reasoning about vectors and learners. Semantically, it introduces a general interpretation function that can be instantiated to define loss functions arising from different existing DLs. We use LDL to establish several theoretical properties of existing DLs, and to conduct their empirical study in neural network verification.

show abstract

Section: Soundness and Completeness Of Dlsmentioning

confidence: 99%

Logic of Differentiable Logics: Towards a Uniform Semantics of DL

Ślusarz¹,

Komendantskaya²,

Daggitt³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…However, as LDL is equipped with quantifiers such a procedure is no longer decidable, we may no longer rely on this method. For a typed FOL, one could define a Kripke-style semantics [36,27] for characterising the set of all true formulae, or take provable FOL formulae to characterise the set of true FOL formulae. In this section we take the latter approach.…”

Section: Soundness and Completeness Of Dlsmentioning

confidence: 99%

Logic of Differentiable Logics: Towards a Uniform Semantics of DL

Ślusarz¹,

Komendantskaya²,

Daggitt³

et al.

EPiC Series in Computing

View full text Add to dashboard Cite

Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates expressions in the syntax into loss functions. These loss functions can then be used during training with standard gradient descent algorithms. The variety of existing DLs and the differing levels of formality with which they are treated makes a systematic comparative study of their properties and implementations difficult. This paper remedies this problem by suggesting a meta-language for defining DLs that we call the Logic of Differentiable Logics, or LDL. Syntactically, it generalises the syntax of existing DLs to FOL, and for the first time introduces the formalism for reasoning about vectors and learners. Semantically, it introduces a general interpretation function that can be instantiated to define loss functions arising from different existing DLs. We use LDL to establish several theoretical properties of existing DLs and to conduct their empirical study in neural network verification.

show abstract

Kripke semantics for higher-order type theory applied to constraint logic programming languages

Cited by 2 publications

References 43 publications

Logic of Differentiable Logics: Towards a Uniform Semantics of DL

Logic of Differentiable Logics: Towards a Uniform Semantics of DL

Logic of Differentiable Logics: Towards a Uniform Semantics of DL

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