Abstract
We ask why Horn clause logic is useful for logic programming. The main reasons seem to lie in a connection between Horn clause logic and algebraic closure operators, and in the fact that recursively enumerable sets can be encoded in initial models of Horn clause theories. The existence of good algorithms for handling algebraic closure operators is also important. We review the other main characteristic properties of Horn clause logic, and ask what they are good for in logic programming and more generally in computer science. We make some polemical remarks about generic models, generalisations of Horn clause logic, and the Byrne-Johnson-Laird theory of syllogisms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kuehner D. Some special purpose resolution systems. In: Meltzer B, Michie D (eds) Machine Intelligence. Halsted Press New York, 1972, pp 117–128.
Henschen LJ, Wos L. Unit refutations and Horn sets. JACM 1974; 21:590–605.
McKinsey JCC. The decision problem for some classes of sentences without quantifiers. J Symbolic Logic 1943; 8:61–76.
Miller D. Abstractions in logic programs. In: Odifreddi P (ed) Logic and Computer Science. Academic Press London, 1990, pp 329–359.
Makowsky JA. Why Horn formulas matter in computer science: initial structures and generic examples. J Comp Sys Sci 1987; 34:266–292.
Mal’tsev AI. Quasiprimitive classes of abstract algebras (Russian). Doklady Akad Nauk SSSR 1956; 108:187–189. Translated in Mal’cev AI. The Metamathematics of Algebraic Systems. North-Holland Amsterdam, 1971, pp 27–31.
Reichel H. Initially restricting algebraic theories. In: Dembinski P (ed) Proc. 9th MFCS, Ryszyna, Lecture Notes in Comp Sci 88. Springer Berlin, 1980, pp 504–514.
Colmerauer A. An introduction to Prolog III. In: Lloyd JW (ed) Computational Logic. Springer Berlin, 1990, pp 37–79.
Post E. Recursively enumerable sets of positive integers and their decision problems. Bull Amer Math Soc 1944; 50:284–316.
Cohn PM. Universal Algebra. Reidel, Dordrecht, 1981.
Kowalski RA. Logic for Problem Solving. North-Holland, New York, 1979.
Smullyan RM. On definability by recursion. Bull Amer Math Soc 1956; 62:601.
Chang CL. The unit proof and the input proof in theorem proving. JACM 1970; 17; 698–708.
Nadathur G, Miller D. Higher-order Horn clauses. JACM 1990; 37:777–814.
Grassmann HG. Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik dargestellt und durch Anwendungen auf die übrigen Zweige der Mathematik, wie auch auf Statik, Mechanik, die Lehre von Magnetismus und die Krystallonomie erläutert. Stettin 1844.
Van Emden MH, Kowalski RA. The semantics of predicate logic as a programming language. JACM 1976; 23:733–742.
Lloyd JW. Foundations of logic programming. Springer, Berlin, 1984.
Minker J. On indefinite databases and the closed world assumption. In: Loveland DW (ed) 6th Conference on Automated Deduction. Springer Berlin, 1982, pp 292–308 (Lecture Notes in Comp Sci 138).
Shepherdson JC. Negation in logic programming. In: Minker J (ed) Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, Los Altos, 1988, pp 19–88.
Johnson-Laird PN, Byrne RMJ. Deduction. Lawrence Erlbaum Associates, Hove and London, 1991.
Ehrig H, Mahr B. Fundamentals of algebraic specification I. Springer Berlin, 1985.
Tarlecki A. On the existence of free models in abstract algebraic institutions. Theor Comp Sci 1985; 37:269–304.
Galvin F. Horn sentences. Ann Math Logic 1970; 1:389–422.
Fagin R. Horn clauses and database dependencies. JACM 1982; 29:952–985.
Volger H. Preservation theorems for limits of structures and global sections of sheaves of structures. Math Zeitschrift 1979; 166:27–53.
Barr M. Models of Horn theories. In: Gray JW, Scedrov A (eds) Categories in Computer Science and Logic. Contemporary Mathematics 92. Amer Math Soc 1989, pp 1–7.
Meinke K. Universal algebra in higher types. Theor Comp Sci (to appear).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 British Computer Society
About this paper
Cite this paper
Hodges, W. (1993). Horn Clause Logic 1992. In: Broda, K. (eds) ALPUK92. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3421-3_12
Download citation
DOI: https://doi.org/10.1007/978-1-4471-3421-3_12
Publisher Name: Springer, London
Print ISBN: 978-3-540-19783-6
Online ISBN: 978-1-4471-3421-3
eBook Packages: Springer Book Archive