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A logic of nonmonotone inductive definitions

Marc Denecker, Eugenia Ternovska
2008 ACM Transactions on Computational Logic  
in a new logic for Non-Monotone Inductive Definitions (ID-logic).  ...  Well-known principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over well-founded sets and iterated induction.  ...  However, there are forms of nonmonotone induction which are quite common in mathematics that are not modelled well by fixpoint logics.  ... 
doi:10.1145/1342991.1342998 fatcat:265gngzzhnealdwfqk6v3mjqre

The nonmonotonic Gentzen deduction systems for the propositional logic

Cungen Cao, Yuefei Sui, Yuhui Wang
2016 Artificial intelligence research  
With the same logical language as, the same valuation as and the validity of a sequent different from the traditional propositional logic, a propositional logic could be nonmonotonic.  ...  their dualities of the validity of sequents, among which one is traditional and others are variations of the traditional one.  ...  We found that each nonmonotonic logic has the occurrence ofA.  ... 
doi:10.5430/air.v5n2p111 fatcat:lmnxxlposreapakgxiwaqkqbnq

Handling Exceptions in nonmonotonic reasoning

Marcelino C. Pequeno, Rodrigo de Melo Souza Veras, Wladimir A. Tavares
2007 Latin-American Workshop on Non-Monotonic Reasoning  
Restricted to the language of general logic programs, DLEF, Reiter's default logic and answer set programming all coincide.  ...  DLEF is our own variant for default logic complying with EFP. We also show alternative definitions for Reiter's default logics and its justified and constrained variants within our framework.  ...  Acknowledgements We are grateful to the anonymous referees of the Third Latin American Workshop on Non-Monotonic Reasoning (LANMR'07) for the valuable comments which helped to improve this paper.  ... 
dblp:conf/lanmr/PequenoVT07 fatcat:pkarumafhvdhdooxxkbyprry74

Induction and Confirmation Theory: An Approach based on a Paraconsistent Nonmonotonic Logic

Ricardo Sousa Silvestre
2011 Princípios  
We pick up one of the most wide-spread nonmonotonic formalisms – default logic – and analyze to what extent and under what adjustments it could work as a logic of induction in the philosophical sense.  ...  By making use of this analysis, we extend default logic so as to make it able to minimally perform the task of a logic of induction, having as a result a system which we believe has interesting properties  ...  of being called a logic of induction or a calculus of inductive implication: Definition 9.  ... 
doaj:fce609c5faa948e3b3a56efa667ff8e3 fatcat:kpcogg5l2vhqdkcbe76a4dbfyq

Ordering Default Theories

Chiaki Sakama
2003 International Joint Conference on Artificial Intelligence  
In the context of default logic, a theory contains default information as well as definite information.  ...  The technique is also applied to order nonmonotonic logic programs.  ...  Ordering default theories thus has potential application to the theory of induction in nonmonotonic logics and nonmonotonic inductive logic programming.  ... 
dblp:conf/ijcai/Sakama03 fatcat:wuauurtbaneqnp6otfvq2cimce

Ordering default theories and nonmonotonic logic programs

Chiaki Sakama
2005 Theoretical Computer Science  
In default logic, on the other hand, a theory contains default information as well as definite information.  ...  The results of this paper provide a method for comparing default theories or nonmonotonic logic programs in a manner different from the conventional extension/model-based viewpoint.  ...  Ordering default theories and nonmonotonic logic programs thus has potential application to the theory of induction in nonmonotonic logics and nonmonotonic inductive logic programming.  ... 
doi:10.1016/j.tcs.2004.12.003 fatcat:of3datz6ezh2tmuldce7jwdqni

Inductive equivalence in clausal logic and nonmonotonic logic programming

Chiaki Sakama, Katsumi Inoue
2010 Machine Learning  
Conditions of inductive equivalence change depending on the logic of representation languages and the logic of induction or inductive logic programming (ILP).  ...  Keywords Inductive equivalence · Inductive logic programming · Nonmonotonic logic programs Introduction Equivalence relations between logical theories have been studied in many ways in artificial intelligence  ...  A Horn clause is called a definite clause if it contains exactly one atom in its head. A definite logic program is a set of definite clauses.  ... 
doi:10.1007/s10994-010-5189-4 fatcat:vxaidrnzg5brle4rxdazclg4pu

Induction of the Effects of Actions by Monotonic Methods [chapter]

Ramon P. Otero
2003 Lecture Notes in Computer Science  
To cope with the frame problem induction under suitable nonmonotonic formalisms has to be used, though this kind of induction is not well understood yet.  ...  Induction of the effects of actions considered here consists in learning an action description of a dynamic system from evidence on its behavior.  ...  (Correspondence Extended) From evidence on narratives consistent, H I is a solution of nonmonotonic induction with inertia (Definition 9) if and only if it is a solution of monotonic induction (Definition  ... 
doi:10.1007/978-3-540-39917-9_20 fatcat:ax7s62jzorcxzad6cxfqgn7hqm

On Priest on Nonmonotonic and Inductive Logic

Greg Restall
2016 Thought: A Journal of Philosophy  
Priest's favoured way out of this tension is to adopt a nonmonotonic logic, LPm.  ...  Graham Priest defends the use of a nonmonotonic logic, LPm, in his analysis of reasoning in the face of true contradictions, such as those arising from the paradoxes of self-reference.  ...  LPm is a nonmonotonic (aka inductive) logic. And it is precisely the definition of such logics that they may lead us from truth to untruth.  ... 
doi:10.1002/tht3.201 fatcat:hdfblwbiebbfvdtjokkiu65e3m

Extending Classical Logic with Inductive Definitions [article]

Marc Denecker
2000 arXiv   pre-print
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships  ...  to other logics in the area of non-monotonic reasoning, logic programming and deductive databases, and to show its application for knowledge representation by giving a typology of definitional knowledge  ...  This paper defines and investigates a conservative extension of classical logic with a less general nonmonotonic closure principle: the principle of definition and inductive definition.  ... 
arXiv:cs/0003019v1 fatcat:svyilctko5hprckbrzjvpcc7ee

Page 6002 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
In this paper, we make a first step in this direction by specifying a nonmonotonic extension of a simple terminological logic.”  ...  While nonmonotonic inheritance networks formalize the notion of default inheritance of typical properties, terminological logics formalize the notion of defining concepts and reasoning about definitions  ... 

Page 6093 of Mathematical Reviews Vol. , Issue 98J [page]

1998 Mathematical Reviews  
Then the formal definition of default models is introduced, and representation theorems for the system are stated. Next, the syntax and semantics of the new logic are presented.  ...  6093 logic whose leading principle is to prepare means for modelling of the vagueness phenomenon. The latter is a logic of common sense human reasoning which is based on the use of natural language.  ... 

Induction from answer sets in nonmonotonic logic programs

Chiaki Sakama
2005 ACM Transactions on Computational Logic  
This article studies a method for realizing induction in nonmonotonic logic programs.  ...  The proposed methods extend the present ILP techniques to a syntactically and semantically richer framework, and contribute to a theory of nonmonotonic ILP.  ...  In fact, their definition of induction from negative examples is identical to the definition of induction from positive examples.  ... 
doi:10.1145/1055686.1055687 fatcat:nuunsarv5vfutgdone2fscb52y

First-order jk-clausal theories are PAC-learnable

Luc De Raedt, Sašo Džeroski
1994 Artificial Intelligence  
We present positive PAC-learning results for the nonmonotonic inductive logic programming setting.  ...  Finally, we compare our results to PAC-learnability results for the normal inductive logic programming setting. * First version January 1994, second and revised version May 1994.  ...  CIPA3510920370, and PECO Scientific Network on Inductive Logic Programming CIPA3510OCT920044.  ... 
doi:10.1016/0004-3702(94)90112-0 fatcat:5lpp7hoixjbrdkgnsstjhs34ya

A simple sequent calculus for partial functions

Morten Elvang-Gøransson, Olaf Owe
1993 Theoretical Computer Science  
Owe, A simple sequent calculus for partial functions, Theoretical  ...  Salvesen has provided useful feedback through careful reading of a draft version.  ...  Owe By the requirement that free variables range over defined values only, and by the inductive definition of definedness, we avoid the introduction of nonmonotonic connectives in the base logic.  ... 
doi:10.1016/0304-3975(93)90077-7 fatcat:oitr2pecwffzbmrc5b4hmxyysa
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