Non-monotonic logic
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A non-monotonic logic is a
Abductive reasoning
Abductive reasoning is the process of deriving a sufficient explanation of the known facts. An abductive logic should not be monotonic because the likely explanations are not necessarily correct. For example, the likely explanation for seeing wet grass is that it rained; however, this explanation has to be retracted when learning that the real cause of the grass being wet was a sprinkler. Since the old explanation (it rained) is retracted because of the addition of a piece of knowledge (a sprinkler was active), any logic that models explanations is non-monotonic.
Reasoning about knowledge
If a logic includes formulae that mean that something is not known, this logic should not be monotonic. Indeed, learning something that was previously not known leads to the removal of the formula specifying that this piece of knowledge is not known. This second change (a removal caused by an addition) violates the condition of monotonicity. A logic for reasoning about knowledge is the autoepistemic logic.
Belief revision
Proof-theoretic versus model-theoretic formalizations of non-monotonic logics
See also
Notes
- ^ Strasser, Christian; Antonelli, G. Aldo. "Non-Monotonic Logic". plato.stanford.edu/index.html. Stanford Encyclopedia of Philosophy. Retrieved 19 March 2015.
- ^ a b Suchenek, Marek A. (2011), "Notes on Nonmonotonic Autoepistemic Propositional Logic" (PDF), Zeszyty Naukowe (6), Warsaw School of Computer Science: 74–93.
- ^ a b Suchenek, Marek A. (1993), "First-order syntactic characterizations of minimal entailment, domain-minimal entailment, and Herbrand entailment", Journal of Automated Reasoning (10), Kluwer Academic Publishers / Springer: 237–263.
References
- Bidoit, N.; Hull, R. (1989). "Minimalism, justification and non-monotonicity in deductive databases". .
- Brewka, G. (1991). Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press. ISBN 978-0-521-38394-3.
- Brewka, G.; Dix, J.; Konolige, K. (1997). Nonmonotonic Reasoning — An Overview. CSLI Lecture Notes. Vol. 73. Stanford: CSLI publications. ISBN 9781881526834.
- Cadoli, M.; Schaerf, M. (1993). "A survey of complexity results for non-monotonic logics". .
- Donini, F.M.; Lenzerini, M.; Nardi, D.; Pirri, F.; Schaerf, M. (1990). "Nonmonotonic reasoning". Artificial Intelligence Review. 4 (3): 163–210. S2CID 23575942.
- ISBN 978-3-642-82453-1.
- Ginsberg, M.L., ed. (1987). Readings in Nonmonotonic Reasoning. Morgan Kaufmann. ISBN 978-0-934613-45-3.
- Horty, J.F. (2001). "Nonmonotonic Logic". In Goble, Lou (ed.). The Blackwell Guide to Philosophical Logic. Wiley. ISBN 978-0-631-20692-7.
- Łukaszewicz, W. (1990). Non-Monotonic Reasoning. Ellis-Horwood. ISBN 978-0-13-624446-2.
- Lundberg, C.G. (2000). "Made sense and remembered sense: Sensemaking through abduction" (PDF). Journal of Economic Psychology. 21 (6): 691–709. S2CID 11723465. Archived from the original(PDF) on 2017-09-07.
- Makinson, D. (2005). Bridges from Classical to Nonmonotonic Logic. College Publications. ISBN 9781904987000.
- Marek, W.; Truszczynski, M. (1993). Nonmonotonic Logics: Context-Dependent Reasoning. Springer. ISBN 978-3-662-02906-0.
- Abdallah, A. Nait (1995). The Logic of Partial Information. Springer. ISBN 978-3-642-78160-5.
- Suchenek, Marek A. (1993). "First-order syntactic characterizations of minimal entailment, domain-minimal entailment, and Herbrand entailment". Journal of Automated Reasoning. 10 (2). Kluwer Academic Publishers / Springer: 237–263. .
External links
- Antonelli, G. Aldo. "Non-monotonic logic". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
- Non-monotonic logic at PhilPapers
- Non-monotonic logic at the Indiana Philosophy Ontology Project