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Propositions with Typed Lambda Calculus λ

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Abstract

The aim of the paper is to study simple and compound propositions in English and Punjabi, and also discuss the suitability and applicability of typed lambda calculus λ. We select randomly ten simple and ten compound propositions and evaluate them by applying function application particularly value description and β-reduction according to Coppock and Champollion (Invitation to Formal Semantics, 2021, http://eecoppock.info/teaching.html). We point out that a single ‘BE’ predicate dominates all simple propositions, while compound propositions contain different predicates. The final results record as ≤ 1 and 0.3, 0.1 in simple and compound propositions, respectively.

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Notes

  1. The place of lambda terms and conversion rules take significant place in lambda calculus. The following way we understand lambda terms.

    (a) Variables = v0, v1,…….

    (b) Abstractor = λ.

    (c) Parenthesis = (,) [1].

  2. The following types show the conversion rules as:

    M → N in favour of α = conversion happens from left to right.

    M ← N in favour of α = conversion happens from right to left.

    M ↔ N in favour of α = conversion happens in both sides.

  3. Punjabi is a modern Indo-Aryan language. It is only selected for translation purpose from English. Remember that final analysis would go along with English while describing the simple and compound propositions.

  4. Consider ℼ and α are expressions where one is the function and another is input type, and they appear before us as ℼ (α) which means that ℼ as function applies on to α.

  5. Do not confuse with SN (1–10) on left side, we consider total 10-10 two sets of simple and compound propositions in English, and remember that they also appear as 20 in Table 2 and with predicates-I, II in Table 3.

References

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Authors and Affiliations

  1. Indira Gandhi National Tribal University, Amarkantak, MP, 484887, India

    Harjit Singh

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  1. Harjit Singh
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Correspondence to Harjit Singh.

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This study is not conducted under any funding agency so far. I declared that there is no “conflict of interest” regarding any grants or funding agency.

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This article is part of the topical collection “Advances in Machine Vision and Augmented Intelligence” guest edited by Manish Kumar Bajpai, Ranjeet Kumar, Koushlendra Kumar Singh, and George Giakos.

Appendix-I

Appendix-I

See Table 5.

Table 5 Final output of propositions in typed lambda calculus λ
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Singh, H. Propositions with Typed Lambda Calculus λ. SN COMPUT. SCI. 3, 204 (2022). https://doi.org/10.1007/s42979-022-01056-6

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