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Logic Operators and Quantifiers in Type-Theory of Algorithms

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Logic and Engineering of Natural Language Semantics (LENLS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14213))

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Abstract

In this work, I introduce the Type-Theory of Algorithms (TTA), which is an extension of Moschovakis Type-Theory of Algorithms and its reduction calculus, by adding logic operators and quantifiers. The formal language has two kinds of terms of formulae, for designating state-independent and state-dependent propositions and predications. The logic operators include conjunction, disjunction, conditional implication, and negation. I add state-dependent quantifiers, for enhancing the standard quantifiers of predicate logic. I provide an extended reduction calculus of the Type-Theory of Acyclic Algorithms, for reductions of terms to their canonical forms. The canonical forms of the terms provide the algorithmic semantics for computing the denotations.

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Notes

  1. 1.

    There are other possibilities for the truth values of the erroneous truth value \( er \) for the quantifiers, which we do not consider in this paper.

  2. 2.

    https://www.scheme.com/tspl4/start.html#./start:h4,.

  3. 3.

    https://www.haskell.org.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street, Block 8, 1113, Sofia, Bulgaria

    Roussanka Loukanova

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  1. Roussanka Loukanova
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Correspondence to Roussanka Loukanova .

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Editors and Affiliations

  1. Ochanomizu University, Tokyo, Japan

    Daisuke Bekki

  2. Keio University, Tokyo, Japan

    Koji Mineshima

  3. Aoyama Gakuin University, Tokyo, Japan

    Elin McCready

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Loukanova, R. (2023). Logic Operators and Quantifiers in Type-Theory of Algorithms. In: Bekki, D., Mineshima, K., McCready, E. (eds) Logic and Engineering of Natural Language Semantics. LENLS 2022. Lecture Notes in Computer Science, vol 14213. Springer, Cham. https://doi.org/10.1007/978-3-031-43977-3_11

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  • DOI: https://doi.org/10.1007/978-3-031-43977-3_11

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  • Print ISBN: 978-3-031-43976-6

  • Online ISBN: 978-3-031-43977-3

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