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Indefinite Reasoning with Definite Rules

L. Thorne McCarty, Ron van der Meyden
1991 International Joint Conference on Artificial Intelligence  
Adopting this point of view, we show that first-order logic is insufficiently expressive to handle important examples of common sense reasoning.  ...  In this paper we present a novel explanation of the source of indefinite information in common sense reasoning: Indefinite information arises from reports about the world expressed in terms of concepts  ...  The proof theory for intuitionistic embedded implications is also a straightforward generalization of the proof theory for classical Horn-clause logic [McCarty, 1988b] .  ... 
dblp:conf/ijcai/McCartyM91 fatcat:2ecufuexqncd5bc2crpgjbrjyy

"Reductio ad absurdum" and Łukasiewicz's modalities

S. P. Odintsov
2003 Logic and Logical Philosophy  
In the definition of C-logics we leave the intuitionistic implication unchanged, therefore, a C-logic meets the paradox of minimal logic if and only if the negation defined via its operator C satisfy the  ...  The classical logic Lk and the logic of classical refutability Le can be axiomatized modulo intuitionistic logic Li and minimal logic Lj, respectively, via either the Peirce law P or the generalized law  ... 
doi:10.12775/llp.2003.008 fatcat:psrwzg2dnzgaxpaqv2rjrmvf4m

Page 1550 of Mathematical Reviews Vol. 57, Issue 4 [page]

1979 Mathematical Reviews  
“The paper presents an algorithm for minimization of weakly defined multiargument logic functions based on the method of quasi-implicants reduction.  ...  In summary, this reviewer finds this to be a worthy tome in the annals of classical network theory.  ... 

LP=>: Extending LP with a strong conditional operator [article]

Nick Thomas
2013 arXiv   pre-print
The resulting logic can speak of consistency in more discriminating ways, but introduces new possibilities for trivializing paradoxes.  ...  We augment LP with a strong conditional operator, to yield a logic we call "strong LP," or LP=>.  ...  in classical logic. 2 Embeddings of classical theories An intended application of LP ⇒ is in constructing inconsistent theories which prove all the theorems of some classical theory, and none of  ... 
arXiv:1304.6467v1 fatcat:zmdezskmlvhinlxo7ynptuz64i

Circumscribing embedded implications (without stratifications)

L.Thorne McCarty
1993 The Journal of Logic Programming  
This paper is a study of circumscription, not in classical logic, as usual, but in intuitionistic logic.  ...  We first review the intuitionistic circumscription of Horn clause logic programs, which was discussed in previous work, and we then consider the larger class of embedded implications.  ...  Lin defines a form of partial circumscription in classical logic that is virtually identical to our Definition 6.1 when the embedded implications in &I! are restricted to embedded negations.  ... 
doi:10.1016/0743-1066(93)90036-g fatcat:62rlo2fl2rajjpzu3iwcklo4o4

Classical negation can be expressed by one of its halves

J-Y Beziau
1999 Logic Journal of the IGPL  
We present the logic K/2 which is a logic with classical implication and only the left part of classical negation.  ...  We show that it is possible to define a classical negation into K/2 and that the classical propositional logic K can be translated into this apparently weaker logic.  ...  , negation and implication is translatable into classical logic with negation and implication only.  ... 
doi:10.1093/jigpal/7.2.145 fatcat:aw4jgdiqhfbfjpbb6kdxuxwhky

Page 3434 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
Using theorems of mathemati- cal logic, some results about the definability of progressions in minimal action theory are obtained.”  ...  Summary: “We present a method for translating Horn clauses ex- tended with modalities and embedded implication (which provide reasoning capabilities in a multi-agent situation and hypothetical reasoning  ... 

A proof-theoretic foundation of abortive continuations

Zena M. Ariola, Hugo Herbelin, Amr Sabry
2007 Higher-Order and Symbolic Computation  
We then move on to the computational side and emphasize that Parigot's λµ corresponds to minimal classical logic. A continuation constant must be added to λµ to get full classical logic.  ...  We give an analysis of various classical axioms and characterize a notion of minimal classical logic that enforces Peirce's law without enforcing Ex Falso Quodlibet.  ...  Depending on whether EFQ, PL, or both are assumed in minimal logic, we get intuitionistic, minimal classical, or classical logic.  ... 
doi:10.1007/s10990-007-9007-z fatcat:msxempufgnabzgahcdhq3clpm4

On Various Negative Translations

Gilda Ferreira, Paulo Oliva
2011 Electronic Proceedings in Theoretical Computer Science  
In this derived ordering, Kuroda and Krivine are minimal elements.  ...  Several proof translations of classical mathematics into intuitionistic mathematics have been proposed in the literature over the past century.  ...  On intuitionistic versus minimal logic More than translating CL into IL, it is well known that some negative translations produce embeddings of CL into minimal logic ML (i.e. intuitionistic logic without  ... 
doi:10.4204/eptcs.47.4 fatcat:y45zb5zhsvdcnge5rxwxc7slxu

Page 938 of Mathematical Reviews Vol. , Issue 82c [page]

1982 Mathematical Reviews  
(In particular, the same negated formulae are provable in intuitionistic and classical propositional logic.) This result fails if “intuitionistic” is replaced by “minimal” (take A to be = p—>p).  ...  The authors present an algorithm for the reverse process in this general situation. The set of formulas produced by the algorithm is minimal and complete with respect to implication.  ... 

Page 913 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Nawaz [in Non-classical logics and their applications to fuzzy subsets (Linz, 1992), 159-217, Kluwer Acad.  ...  Rasiowa stated without proof that in implicative algebras there is a one-to-one correspon- dence between kernels of epimorphisms and the so-called special implicative filters, and that in the logic whose  ... 

Page 4392 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
Popov, An embedding of an implicative fragment of classical logic into an implicative fragment of intuitionistic logic (Russian) (80-83); A. V.  ...  Vasyukov, Implicative logics, Lambek systems, and exponential multicategories (Rus- sian) (90-118); S. P. Odintsov, On negatively equivalent extensions of minimal logic (Russian) (119-127); V. M.  ... 

General default logic

Yi Zhou, Fangzhen Lin, Yan Zhang
2009 Annals of Mathematics and Artificial Intelligence  
We show that this logic is a generalization of Reiter's default logic [1] and Gelfond et al.'s disjunctive default logic [2] in propositional case.  ...  In this paper, we present a logic R for rule bases by introducing a set of rule connectives. We define both the models and extensions of a rule base.  ...  The second author is supported in part by a Croucher Senior Research Fellowship and by HK RGC under grant HKUST CERG 616806.  ... 
doi:10.1007/s10472-009-9161-6 fatcat:ve6xpoggbjeyxn2rnhnyigq5am

Applications of Annotated Predicate Calculus to Querying Inconsistent Databases [chapter]

Marcelo Arenas, Leopoldo Bertossi, Michael Kifer
2000 Lecture Notes in Computer Science  
This is done by simultaneously embedding the database and the integrity constraints, which are mutually inconsistent in classical logic, into a theory in annotated predicate calculus -a logic that allows  ...  In this way, several goals are achieved: (a) A logical specification of the class of all minimal "repairs" of the original database, and the ability to reason about them; (b) The ability to distinguish  ...  The most useful types of embeddings are those where theories that are inconsistent in classical logic become consistent in APC.  ... 
doi:10.1007/3-540-44957-4_62 fatcat:vduxxjho7fa57aackh2bsjwdlu

Logic of classical refutability and class of extensions of minimal logic

Sergei P. Odintsov
2004 Logic and Logical Philosophy  
In Section 2 of the present article, we consider the Grzegorczyk-style semantics for Le which vividly demonstrates that minimal logic Lj relates to logic of classical refutability Le essentially in the  ...  Therefore, we may consider minimal logic as a positivistic approximation of logic of classical refutability and suppose that classical logic and Le have common ontological presuppositions except for the  ... 
doi:10.12775/llp.2001.006 fatcat:l5jkrmg5rbeedmu3t7kzmdghn4
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