Keywords
logical connectives
computational logic
artificial intelligence reasoning
symbolic and operational logic integration
How to Cite
Abstract
Philosophical logic has traditionally been conceived as a normative discipline concerned with the principles of valid reasoning, truth preservation, and the formal structure of arguments. From its classical foundations in Aristotelian syllogistic reasoning to its formalisation in the works of Frege, Tarski, and Gödel, logic has been treated as an abstract and implementation-independent framework. However, the emergence and rapid development of computer science have significantly transformed both the scope and interpretation of logic. Rather than functioning solely as a theoretical guide to correct reasoning, logic has become an operational and computational tool embedded in modern technological systems. This paper provides a comprehensive and integrated analysis of the relationship between philosophical logic and computer science, with particular emphasis on the role of logical connectives, namely, conjunction, disjunction, implication, biconditional, and negation, as foundational elements bridging abstract reasoning and practical computation. It examines how these connectives underpin Boolean algebra, digital circuit design, programming languages, database systems, and web technologies such as HTML, CSS, Bootstrap, and JavaScript. Furthermore, the paper explores the extension of logical principles into artificial intelligence, where they support knowledge representation, automated reasoning, and decision-making processes. Beyond applications, the study argues that computer science does not merely apply logic but actively reshapes it. Developments such as the Curry–Howard correspondence, resource-sensitive logics, dynamic and temporal logics, and computational semantics demonstrate that logic is increasingly procedural, context-sensitive, and execution-oriented. Consequently, logic must now be understood as a hybrid normative–computational discipline that integrates abstract reasoning with algorithmic processes. The paper concludes that the future of logic lies in its continued interaction with computational practice, where philosophical insights and technological innovations jointly redefine the nature of reasoning, meaning, and intelligent systems.
References
Aristotle. (1984). The Complete Works of Aristotle (J. Barnes, Ed.). Princeton University Press.
Baader, F., Calvanese, D., McGuinness, D. L., Nardi, D., & Patel-Schneider, P. F. (2003). The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press.
Berners-Lee, T., Hendler, J., & Lassila, O. (2001). The Semantic Web. Scientific American, 284(5), 34–43.
Bobzien, S. (1996). Stoic Logic. Oxford University Press.
Boole, G. (1854). An Investigation of the Laws of Thought on Which Are Founded the Mathematical Theories of Logic and Probabilities. Walton and Maberly.
Church, A. (1936). An unsolvable problem of elementary number theory. American Journal of Mathematics, 58(2), 345–363.
Clarke, E. M., Emerson, E. A., & Sistla, A. P. (1986). Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Transactions on Programming Languages and Systems, 8(2), 244–263.
Elmasri, R., & Navathe, S. B. (2017). Fundamentals of Database Systems (7th ed.). Pearson.
Frege, G. (1879). Begriffsschrift: A Formula Language Modeled upon That of Arithmetic for Pure Thought. Halle: Nebert.
Gentzen, G. (1935). Investigations into logical deduction. Mathematische Zeitschrift, 39, 176–210, 405–431.
Girard, J.-Y. (1987). Linear logic. Theoretical Computer Science, 50(1), 1–101.
Gödel, K. (1931). On formally undecidable propositions of Principia Mathematica and related systems. Monatshefte für Mathematik und Physik, 38, 173–198.
Harel, D., Kozen, D., & Tiuryn, J. (2000). Dynamic Logic. MIT Press.
Harper, R. (2012). Practical Foundations for Programming Languages. Cambridge University Press.
Hilbert, D. (1928). The foundations of mathematics. In From Frege to Gödel: A Source Book in Mathematical Logic (pp. 464–479). Harvard University Press.
Howard, W. A. (1980). The formulae-as-types notion of construction. In J. P. Seldin & J. R. Hindley (Eds.), To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (pp. 479–490). Academic Press.
Huth, M., & Ryan, M. (2020). Logic in Computer Science: Modelling and Reasoning about Systems (3rd ed.). Cambridge University Press.
Lloyd, J. W. (1987). Foundations of Logic Programming (2nd ed.). Springer.
Mano, M. M., & Ciletti, M. D. (2018). Digital Design (6th ed.). Pearson.
Martin-Löf, P. (1984). Intuitionistic Type Theory. Bibliopolis.
Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann.
Quine, W. V. O. (1986). Philosophy of Logic (2nd ed.). Harvard University Press.
Reiter, R. (1980). A logic for default reasoning. Artificial Intelligence, 13(1–2), 81–132.
Russell, S., & Norvig, P. (2021). Artificial Intelligence: A Modern Approach (4th ed.). Pearson.
Shortliffe, E. H. (1976). Computer-Based Medical Consultations: MYCIN. Elsevier.
Sørensen, M. H., & Urzyczyn, P. (2020). Lectures on the Curry–Howard Isomorphism (2nd ed.). Elsevier.
Tarski, A. (1935). The concept of truth in formalized languages. In Logic, Semantics, Metamathematics (1956 ed.). Oxford University Press.
Turing, A. M. (1936). On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 42(2), 230–265.
van Benthem, J. (2011). Logical Dynamics of Information and Interaction. Cambridge University Press.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright (c) 2026 Oseni Taiwo Afisi