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Abstract We investigate (co-) induction in classical logic under the propositions-as-types paradigm, considering propositional, second-order and (co-) inductive types. Specifically, we introduce an extension of the Dual Calculus with a Mendler-style (co-) iterator and show that it is strongly normalizing. We prove this using a reducibility argument.
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Kaminsky, Jack. "Logic, Induction, and Ontology." International Studies in Philosophy 20, no. 1 (1988): 111. http://dx.doi.org/10.5840/intstudphil198820151.
Terwijn, Sebastiaan A. "Probabilistic Logic and Induction." Journal of Logic and Computation 15, no. 4 (August 1, 2005): 507–15. http://dx.doi.org/10.1093/logcom/exi032.
Yamaguchi, Fumihiko, and Masakazu Nakanishi. "Induction in linear logic." International Journal of Theoretical Physics 35, no. 10 (October 1996): 2107–16. http://dx.doi.org/10.1007/bf02302230.
Action logic is the algebraic logic (inequational theory) of residuated Kleene lattices. One of the operations of this logic is the Kleene star, which is axiomatized by an induction scheme. For a stronger system that uses an -rule instead (infinitary action logic), Buszkowski and Palka (2007) proved -completeness (thus, undecidability). Decidability of action logic itself was an open question, raised by Kozen in 1994. In this article, we show that it is undecidable, more precisely, -complete. We also prove the same undecidability results for all recursively enumerable logics between action logic and infinitary action logic, for fragments of these logics with only one of the two lattice (additive) connectives, and for action logic extended with the law of distributivity.
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K.M.MAKWANA, K. M. MAKWANA, Dr B. R. PAREKH Dr.B.R.PAREKH, and SHEETAL SHINKHEDE. "Fuzzy Logic Controller Vs Pi Controller for Induction Motor Drive." Indian Journal of Applied Research 3, no. 7 (October 1, 2011): 315–18. http://dx.doi.org/10.15373/2249555x/july2013/97.
Arieli, Itai, and Robert J. Aumann. "The logic of backward induction." Journal of Economic Theory 159 (September 2015): 443–64. http://dx.doi.org/10.1016/j.jet.2015.07.004.
Hill, Alexandra. "Reasoning by analogy in inductive logic." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/reasoning-by-analogy-in-inductive-logic(039622d8-ab3f-418f-b46c-4d4e7a9eb6c1).html.
This thesis investigates ways of incorporating reasoning by analogy into Pure (Unary) Inductive Logic. We start with an analysis of similarity as distance, noting that this is the conception that has received most attention in the literature so far. Chapter 4 looks in some detail at the consequences of adopting Hamming Distance as our measure of similarity, which proves to be a strong requirement. Chapter 5 then examines various adaptations of Hamming Distance and proposes a subtle modification, further-away-ness, that generates a much larger class of solutions.
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Lapointe, Stéphane. "Induction of recursive logic programs." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/7467.
Rowan, Michael. "Hume, probability and induction." Title page, contents and abstract only, 1985. http://web4.library.adelaide.edu.au/theses/09PH/09phr877.pdf.
Caldon, Patrick Computer Science & Engineering Faculty of Engineering UNSW. "Limiting programs for induction in artificial intelligence." Awarded by:University of New South Wales, 2008. http://handle.unsw.edu.au/1959.4/37484.
This thesis examines a novel induction-based framework for logic programming. Limiting programs are logic programs distinguished by two features, in general they contain an infinite data stream over which induction will be performed, and in general it is not possible for a system to know when a solution for any program is correct. These facts are characteristic of some problems involving induction in artificial intelligence, and several problems in knowledge representation and logic programming have exactly these properties. This thesis presents a specification language for problems with an inductive nature, limiting programs, and a resolution based system, limiting resolution, for solving these problems. This framework has properties which guarantee that the system will converge upon a particular answer in the limit. Solutions to problems which have such an inductive property by nature can be implemented using the language, and solved with the solver. For instance, many classification problems are inductive by nature. Some generalized planning problems also have the inductive property. For a class of generalized planning problems, we show that identifying a collection of domains where a plan reaches a goal is equivalent to producing a plan. This thesis gives examples of both. Limiting resolution works by a generate-and-test strategy, creating a potential solution and iteratively looking for a contradiction with the growing stream of data provided. Limiting resolution can be implemented by modifying conventional PROLOG technology. The generateand- test strategy has some inherent inefficiencies. Two improvements have arisen from this work; the first is a tabling strategy which records previously failed attempts to produce a solution and thereby avoids redundant test steps. The second is based on the heuristic observation that for some problems the size of the test step is proportional to the closeness of the generated potential-solution to the real solution, in a suitable metric. The observation can be used to improve the performance of limiting resolution. Thus this thesis describes, from theoretical foundations to implementation, a coherent methodology for incorporating induction into existing general A.I. programming techniques, along with examples of how to perform such tasks.
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Tappert, Peter M. "Damage identification using inductive learning." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-05092009-040651/.
Kimber, Timothy. "Learning definite and normal logic programs by induction on failure." Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/9961.
This thesis presents two novel inductive logic programming (ILP) approaches, based on the notion of a connected theory. A connected theory contains clauses that depend on one another, either directly or via clauses in the background knowledge. Generalisation of such a theory is proved to be a sound and complete method for learning definite ILP hypotheses. The Induction on Failure (IOF) proof procedure, based on the connected theory generalisation method, adds secondary examples into the hypothesis, and generates auxiliary clauses to explain them. These concepts, novel to IOF, address the issues of incompleteness present in previous definite ILP methods. The concept of the connected theory is also applied to the non-monotonic, normal program setting. Thus, the method of generalisation of a normal connected theory is presented. Fundamental to this is the assertion that a partial non-monotonic hypothesis must include both positive and negative information, which the general hypothesis should preserve. This has resulted in, as far as the author is aware, the most complete semantic characterisation available of non-monotonic ILP using a bridge formula. It is proved that generalisation of such a formula to a set of completed definitions is a sound method of generating normal program hypotheses. In the course of establishing a completeness result for this latter approach, the semantics of the supported consequences of a normal program are defined, and the support tree method is presented and shown to be a sound and complete proof procedure for supported consequences. Using these results, it is shown that, for function-free programs, any correct hypothesis for which the examples are supported consequences of the learned program can be derived via a normal connected theory.
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Barnes, Valerie Elizabeth. "The quality of human judgment : an alternative perspective /." Thesis, Connect to this title online; UW restricted, 1985. http://hdl.handle.net/1773/9139.
Barker, Gillian Abernathy. "Abstraction, analogy and induction : toward a general account of ampliative inference /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1997. http://wwwlib.umi.com/cr/ucsd/fullcit?p9820857.
Genesereth, Michael, and Eric Kao. "Induction." In Introduction to Logic, 111–21. Cham: Springer International Publishing, 2012. http://dx.doi.org/10.1007/978-3-031-01798-8_9.
Genesereth, Michael, and Eric Kao. "Induction." In Introduction to Logic, 121–36. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-031-01799-5_9.
Genesereth, Michael, and Eric J. Kao. "Induction." In Introduction to Logic, 121–37. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-031-01801-5_11.
Anthony, Simon, and Alan M. Frisch. "Cautious induction in inductive logic programming." In Inductive Logic Programming, 45–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3540635149_34.
Kotlarski, Henryk. "Transfinite Induction." In Trends in Logic, 73–87. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28921-8_4.
Adriaans, Pieter, and Erik de Haas. "Grammar Induction as Substructural Inductive Logic Programming." In Learning Language in Logic, 127–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-40030-3_8.
Falke, Stephan, and Deepak Kapur. "Inductive Decidability Using Implicit Induction." In Logic for Programming, Artificial Intelligence, and Reasoning, 45–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11916277_4.
Otero, Ramón P. "Induction of Stable Models." In Inductive Logic Programming, 193–205. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44797-0_16.
Conference papers on the topic "Induction (Logic)":
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EELLS, ELLERY. "POPPER AND MILLER, AND INDUCTION AND DEDUCTION." In 7th and 8th Asian Logic Conferences. CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS, 2003. http://dx.doi.org/10.1142/9789812705815_0006.
Eskander, M. N. "Fuzzy logic control of saturated induction machine." In 6th International Workshop on Advanced Motion Control. Proceedings. IEEE, 2000. http://dx.doi.org/10.1109/amc.2000.862878.
Baunsgaard Kristensen, Magnus, Rasmus Ejlers Mogelberg, and Andrea Vezzosi. "Greatest HITs: Higher inductive types in coinductive definitions via induction under clocks." In LICS '22: 37th Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3531130.3533359.
Venkatachalam, M., and S. Thangavel. "Fuzzy logic based performance improvement of induction motor." In 2012 IEEE International Conference on Engineering Education: Innovative Practices and Future Trends (AICERA). IEEE, 2012. http://dx.doi.org/10.1109/aicera.2012.6306749.
Shetgaonkar, Satej Santosh. "Fault diagnosis in induction motor using fuzzy logic." In 2017 International Conference on Computing Methodologies and Communication (ICCMC). IEEE, 2017. http://dx.doi.org/10.1109/iccmc.2017.8282693.
Kuzelka, Ondrej, Jesse Davis, and Steven Schockaert. "Induction of Interpretable Possibilistic Logic Theories from Relational Data." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/160.
The field of statistical relational learning (SRL) is concerned with learning probabilistic models from relational data. Learned SRL models are typically represented using some kind of weighted logical formulas, which makes them considerably more interpretable than those obtained by e.g. neural networks. In practice, however, these models are often still difficult to interpret correctly, as they can contain many formulas that interact in non-trivial ways and weights do not always have an intuitive meaning. To address this, we propose a new SRL method which uses possibilistic logic to encode relational models. Learned models are then essentially stratified classical theories, which explicitly encode what can be derived with a given level of certainty. Compared to Markov Logic Networks (MLNs), our method is faster and produces considerably more interpretable models.
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Abdel-Rahim, Naser M. B. "Fuzzy-Logic control of unsymmetrical two-phase induction motor." In IECON 2012 - 38th Annual Conference of IEEE Industrial Electronics. IEEE, 2012. http://dx.doi.org/10.1109/iecon.2012.6388925.
Madbouly, S. O., H. F. Soliman, H. M. Hasanien, and M. A. Badr. "Fuzzy logic control of brushless doubly fed induction generator." In 5th IET International Conference on Power Electronics, Machines and Drives (PEMD 2010). Institution of Engineering and Technology, 2010. http://dx.doi.org/10.1049/cp.2010.0085.
Johnston, Benjamin, and Guido Governatori. "Induction of defeasible logic theories in the legal domain." In the 9th international conference. New York, New York, USA: ACM Press, 2003. http://dx.doi.org/10.1145/1047788.1047834.
Lukac, Martin. Quantum Inductive Learning and Quantum Logic Synthesis. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.2316.
Computing the least common subsumer (lcs) in description logics is an inference task first introduced for sublanguages of CLASSIC. Roughly speaking, the lcs of a set of concept descriptions is the most specific concept description that subsumes all of the input descriptions. As such, the lcs allows to extract the commonalities from given concept descriptions, a task essential for several applications like, e.g., inductive learning, information retrieval, or the bottom-up construction of KR-knowledge bases. Previous work on the lcs has concentrated on description logics that either allow for number restrictions or for existential restrictions. Many applications, however, require to combine these constructors. In this work, we present an lcs algorithm for the description logic ALEN, which allows for both constructors (as well as concept conjunction, primitive negation, and value restrictions). The proof of correctness of our lcs algorithm is based on an appropriate structural characterization of subsumption in ALEN also introduced in this paper.
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Küsters, Ralf, and Ralf Molitor. Computing Least Common Subsumers in ALEN. Aachen University of Technology, 2000. http://dx.doi.org/10.25368/2022.110.
Computing the least common subsumer (lcs) in description logics is an inference task first introduced for sublanguages of CLASSIC. Roughly speaking, the lcs of a set of concept descriptions is the most specific concept description that subsumes all of the input descriptions. As such, the lcs allows to extract the commonalities from given concept descriptions, a task essential for several applications like, e.g., inductive learning, information retrieval, or the bottom-up construction of KR-knowledge bases. Previous work on the lcs has concentrated on description logics that either allow for number restrictions or for existential restrictions. Many applications, however, require to combine these constructors. In this work, we present an lcs algorithm for the description logic ALEN, which allows for both constructors (as well as concept conjunction, primitive negation, and value restrictions). The proof of correctness of our lcs algorithm is based on an appropriate structural characterization of subsumption in ALEN also introduced in this paper.
