^{1}

^{1}American University of Beirut (Beirut, Lebanon)

DOI: http://doi.org/10.29202/fhi/9/1

Received: January 25, 2018 / Accepted: March 1, 2018 / Published: April 14, 2018

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## Abstract

To illustrate our point, an in-depth attention will in particular be given to the foundational development of the most popular logic programming language, PROLOG, and the Automated Theorem Proving (ATP) systems. Importantly, when studying the interactions between logic and computer science in the literature, we can observe a significant gap in the provision of the appropriate abstraction level. Specifically, we often encounter two different levels of abstraction. The first of these is relatively high even when describing technical notions in computer science, which obviously produces a lack of precision. The second adopts a technical-oriented approach which easily makes the topic and discussion unintuitive or inaccessible to the non-specialist. The paper attempts to remedy these problems by adopting a balanced approach that provides a moderate level of abstraction that targets a deeper understanding of the topic without imposing a very technical presentation on the reader.

Keywords: Frege, Predicate Logic, First Order Logic (FOL), Computer Science, Logic Programming Language, PROLOG, Resolution Principle, Kowalski’s interpretation, Automated Theorem Proving (ATP).

## References

*Un système de communication homme-machine en français*(french human-machine communication system), AI research group, Aix-Marseille university, Luminy.

Curry, Haskell, and Feys, Robert (1958)* Combinatory Logic*. North-Holland.

Curry, Haskell; Hindley Roger, and Seldin Jonathan (1972)* Combinatory Logic*, Volume 2. NorthHolland.

Davis, Martin (1988) Influences of mathematical logic on computer science, In R. Herken, editor, *The Universal Turing Machine: A Half-Century Survey*, 315–326. Oxford University Press.

Davis, Martin (2000) *The Universal Computer*. Norton.

Davis, Martin (2001)* Engines of logic: mathematicians and the origin of the computer*. New York: W.W. Norton & Co..

De Mol, Liesbeth, and Primiero, Giuseppe (2014) Facing computing as technique: towards a history and philosophy of computing. *Philosophy & Technology,* 27, 3, 321-326.

De Mol, Liesbeth, and Primiero, Giuseppe (2015) When logic meets engineering: introduction to logical issues in the history and philosophy of computer science. *History and Philosophy of Logic*, 36 (3), 195-204.

Frege, Gottlob (1879). Begriffsschrift, Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, English translation in Jean van Heijenoort (ed.), *From Frege to Gödel: A Source Book in Mathematical Logi*c, 1879-1931, Harvard University Press, pp. 1-82.

Gillies, Donald (2002) Logicism and the development of computer science. A. C. Kakas and F. Sadri (eds,): *Computational Logic*, Springer-verlag Berlin Heidelberg, pp. 588-604.

Knuth, Donald (1974) Computer science and its relation to mathematics. *American Mathematical Monthly*, 81, 323-343.

Kowalski, Robert (1974)* Predicate logic as programming language*, Proc. IFIP Cong 1974, NorthHolland Pub Co, Amsterdam, 569-574.

Mancosu, Paolo; Zach, Richard, and Badesa, Colixto (2009) The development of mathematical logic from Russell to Tarski, 1900-1935, in: Haaparanta, L., ed., *The development of modern logic*. New York: Oxford University Press, 318-470. Available online: www.ucalgary.ca/rzach/static/history.pdf.

Manna Zohar, and Waldinger Richard (1985)* The Logical Basis for Computer Programming.* Addison-Wesley.

Muggleton, Stephen (ed.) (1992) *Inductive Logic Programming.* Academic Press.

Robinson, John Alan (1965) A Machine-Oriented Logic Based on the Resolution Principle. *Journal for the Association for Computing Machinery,* 12, pp. 23-41.

Robinson, John Alan (2000) *Computational Logic: Memories of the past and challenges for the future*. J.Lloyd et al. (Eds): CL 2000, Springer-Verlag Berlin Heidelberg, 1-24.

Tedre, Matti (2015) *The Science of Computing Shaping a discipline*. Boca Rato: CRC Press.

Ulam, Stanislav (1976) Von Neumann: the interaction of mathematics and computing in: J. Howlett, N. Metropolis and G.-C. Rota, eds., *A History of computing in the twentieth century 1980*, Proceeding of the international research conference on the history of computing, Los Alamos, New York: Academia Press, pp. 93-99.

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*Future Human Image*, Volume 9, 5-19. http://doi.org/10.29202/fhi/9/1