Abstract
This paper investigates inference from evaluable knowledge bases without reasoning by contradiction. These knowledge bases are comprised of non-Horn rules with partial predicates and functions, some of them are defined as recursive functions. This inference corresponds to model elimination without the reduction rule, which is equivalent to forward and backward chaining extended with rule contrapositives, to input resolution, and to constrained resolution without factoring including its ordered variant.
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References
Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Handbook of automated reasoning, vol. 1, pp. 19–99. Elsevier, Amsterdam (2001)
Besnard, P., Hunter, A.: A review of argumentation based on deductive arguments. Handbook of Formal Argumentation, pp. 437–484 (2018)
Brotherston, J., Simpson, A.: Sequent calculi for induction and infinite descent. J. Logic Comput. 21(6), 1177–1216 (2010)
Casas, A., Cabeza, D., Hermenegildo, M.V.: A syntactic approach to combining functional notation, lazy evaluation, and higher-order in LP systems. In: Hagiya, M., Wadler, P. (eds.) FLOPS 2006. LNCS, vol. 3945, pp. 146–162. Springer, Heidelberg (2006). https://doi.org/10.1007/11737414_11
Chang, C.L., Lee, R.C.T.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, Cambridge (1973)
Cohen, L., Rowe, R.N.S.: Uniform inductive reasoning in transitive closure logic via infinite descent. In: 27th EACSL Annual Conference on Computer Science Logic, vol. 119, pp. 17:1–17:16. LIPICS (2018)
Denecker, M., Truszczynski, M., Vennekens, J.: About negation-as-failure and the informal semantics of logic programming. Association for Logic Programming (2017)
Denecker, M., Vennekens, J.: The well-founded semantics is the principle of inductive definition, revisited. In: 14th International Conference on the Principles of Knowledge Representation and Reasoning, AAAI (2014)
Girard, J.Y.: Linear logic. Theor. Comput. Sci. 50(1), 1–101 (1987)
Hanus, M.: Functional logic programming: from theory to curry. In: Voronkov, A., Weidenbach, C. (eds.) Programming Logics. LNCS, vol. 7797, pp. 123–168. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-37651-1_6
Hermenegildo, M.V., et al.: An overview of Ciao and its design philosophy. Theor. Pract. Logic Program. 12(1–2), 219–252 (2012)
Hou, P., De Cat, B., Denecker, M.: FO (FD): extending classical logic with rule-based fixpoint definitions. Theor. Pract. Logic Program. 10(4–6), 581–596 (2010)
Jeřábek, E.: Admissible rules of Łukasiewicz logic. J. Logic Comput. 20(2), 425–447 (2010)
Kakas, A.C., Mancarella, P., Toni, F.: On argumentation logic and propositional logic. Studia Logica 106(2), 237–279 (2018)
Kovács, L., Voronkov, A.: First-order theorem proving and Vampire. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 1–35. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_1
McCune, W.: Otter 3.3 reference manual and guide. Technical report, Argonne National Lab. (2003)
Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. Handbook Autom. Reasoning, vol. 1, pp. 371–443. Elsevier (2001)
Rodríguez-Hortalá, J., Sánchez-Hernández, J.: Functions and lazy evaluation in Prolog. Electron. Notes Theor. Comput. Sci. 206, 153–174 (2008)
Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 3rd edn. Prentice Hall Press, Hoboken (2009)
Sakharov, A.: Hierarchical resolution for structured predicate definitions. In: 11th Hellenic Conference on Artificial Intelligence, pp. 202–210 (2020)
Sakharov, A.: Heuristic backward chaining based on predicate tensorization. In: Silhavy, R. (ed.) CSOC 2021. LNNS, vol. 229, pp. 573–586. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77445-5_52
Schlipf, J.S.: The expressive powers of the logic programming semantics. J. Comput. Syst. Sci. 51(1), 64–86 (1995)
Shen, Y.D., Yuan, L.Y., You, J.H.: SLT-resolution for the well-founded semantics. J. Autom. Reasoning 28(1), 53–97 (2002)
Somogyi, Z., Henderson, F., Conway, T.: The execution algorithm of mercury, an efficient purely declarative logic programming language. J. Logic Program. 29(1–3), 17–64 (1996)
Stickel, M.E.: A Prolog technology theorem prover: a new exposition and implementation in Prolog. Theor. Comput. Sci. 104(1), 109–128 (1992)
Yamasaki, S., Kurose, Y.: A sound and complete procedure for a general logic program in non-floundering derivations with respect to the 3-valued stable model semantics. Theor. Comput. Sci. 266(1–2), 489–512 (2001)
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Sakharov, A. (2021). Inference Methods for Evaluable Knowledge Bases. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds) Software Engineering Application in Informatics. CoMeSySo 2021. Lecture Notes in Networks and Systems, vol 232. Springer, Cham. https://doi.org/10.1007/978-3-030-90318-3_41
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DOI: https://doi.org/10.1007/978-3-030-90318-3_41
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