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Paraconsistent Logic Programs with Four-Valued Rough Sets [chapter]

Jan Małuszyński, Andrzej Szałas, Aida Vitória
2008 Lecture Notes in Computer Science  
This paper presents a language for defining four-valued rough sets and to reason about them. Our framework brings together two major fields: rough sets and paraconsistent logic programming.  ...  On the one hand it provides a paraconsistent approach, based on four-valued rough sets, for integrating knowledge from different sources and reasoning in the presence of inconsistencies.  ...  Our framework relates and brings together two major fields: rough sets [8] and paraconsistent logic programming [3] .  ... 
doi:10.1007/978-3-540-88425-5_5 fatcat:g4mkxinvmfdqdgxyk2tqopzsgm

Defining Rough Sets by Extended Logic Programs [article]

Jan Małuszyński, Aida Vitória (Linköping University, Sweden)
2002 arXiv   pre-print
Thus, we not only show a possible application of a paraconsistent logic to the field of rough sets as we also establish a link between rough set theory and logic programming, making possible transfer of  ...  We show how definite extended logic programs can be used for defining and reasoning with rough sets. Moreover, a rough-set-specific query language is presented and an answering algorithm is outlined.  ...  Each predicate symbol p, with arity n ≥ 0, occurring in P denotes the rough relation (set) For a model theoretic semantics for DXL programs based on the four-valued Belnap's logic the reader is referred  ... 
arXiv:cs/0207089v1 fatcat:ektd2jxajnffjo2yzbifwmwii4

An encompassing framework for Paraconsistent Logic Programs

João Alcântara, Carlos Viegas Damásio, Luís Moniz Pereira
2005 Journal of Applied Logic  
We then define Coherent Answer Sets, and the Paraconsistent Well-founded Model semantics, generalizing many paraconsistent semantics for logic programs.  ...  The T B P J operator determines the value assigned to each propositional symbol Ps J = T B Ps J P J and T B Ps J ). Let P be a paraconsistent logic program and J an interpretation.  ...  These are determined by Rough Sets (cf. [44] ), introduced to deal with imprecise information.  ... 
doi:10.1016/j.jal.2004.07.012 fatcat:e7rhbygxsrhpbgcibudexvo7li

Dominance-Based Rough Set Approach and Bipolar Abstract Rough Approximation Spaces [chapter]

Salvatore Greco, Benedetto Matarazzo, Roman Słowiński
2008 Lecture Notes in Computer Science  
Bipolar Abstract Rough Approximation Spaces Salvatore Greco, Benedetto Matarazzo, Roman Słowinski • Paraconsistent Logic Programs with Four- Valued Rough Sets Jan Małuszynski, Andrzej Szałas, Aida  ...  Vitória • An Equivalent Definition of Rough Sets Guilong Liu, James Kuodo Huang Session RB1: Data Mining I • Inducing Better Rule Sets by Adding Missing Attribute Values Jerzy W.  ... 
doi:10.1007/978-3-540-88425-5_4 fatcat:xcbqwqavsrdfvdkdqflgwhaqj4

A Framework for Reasoning with Rough Sets [chapter]

Aida Vitória
2005 Lecture Notes in Computer Science  
It is then shown that programs in the proposed language can be compiled to extended logic programs under the paraconsistent stable model semantics.  ...  The first problem is related with how to define rough sets in terms of other rough sets. The second problem is related with how to incorporate domain or expert knowledge.  ...  We avoid this problem because each non-recursive rough program with quantitative measures can be compiled to a logic program with at most one paraconsistent stable model.  ... 
doi:10.1007/11574798_10 fatcat:lrk7y3nwe5hhlg3y3pkfkalg34

Three-Valued Logics, Uncertainty Management and Rough Sets [chapter]

Davide Ciucci, Didier Dubois
2014 Lecture Notes in Computer Science  
as rough sets.  ...  Based on the fact that many three-valued logics can be put under a unique algebraic umbrella, we show how to translate three-valued conjunctions and implications into operations on ill-known sets such  ...  Rough Sets: From Modal Logic to Three-Valued Logics Apart from many-valued logics, a natural logical rendering of rough sets is through modal logics.  ... 
doi:10.1007/978-3-642-54756-0_1 fatcat:o7vun6jnzncxrizq3vfwxvji34

The Implications of Paraconsistency

John K. Slaney
1991 International Joint Conference on Artificial Intelligence  
This is a connected scries of arguments concerning paraconsistent logic.  ...  It is argued first that paraconsistency is an option worth pursuing in automated reasoning, then that the most popular paraconsistent logic, fde, is inadequate for the reconstruction of essential first  ...  For the four-valued paraconsistent logic we can keep the classical truth conditions, making B true for V iff for every v-variant V' of V where the order is the relation of material implication as specified  ... 
dblp:conf/ijcai/Slaney91 fatcat:gzprfltharhdrhn22nanyeyhcm

Logical theory revision through data underdetermination: an anti-exceptionalist exercise

Sanderson Molick
2021 Principia: An International Journal of Epistemology  
The resulting picture is coherent with the Laudanean view that agreement and disagreement between scientific theories take place at different levels.  ...  For this, I argue that the ubiquitous nature of logical data is responsible for the proliferation of several distinct methodologies for logical theories.  ...  Gratitude also extends to the audience of the 4th Filomena Workshop, especially to the Bergen Logic Group. The present research was funded by a CAPES Scholarship. Process: 88887.161384/2017-00.  ... 
doi:10.5007/1808-1711.2021.e80110 fatcat:vd7hdkgedvcefg6hs4b62mt22u

Paraconsistent Justification Logic: a Starting Point

Che-Ping Su
2014 Advances in Modal Logic  
We call the logic to be developed paraconsistent justification logic. The hope is that this logic could help us better model belief revision.  ...  In addition, the main technical result of the paper is that quasi-realization theoremwhich holds for standard two-valued justification logic systems -also holds for this three-valued system.  ...  (t • s 1 ) • s 2 . . . ) • s n Joseph Lurie also independently comes up with the idea of merging justification logic with paraconsistent logic.  ... 
dblp:conf/aiml/Su14 fatcat:snm52ghsznfedamp7aoa6fsaem

Page 23 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
Prefer- ence logics; 3. Nonmonotonic inference relations; 4. Consistency- based logics; 5. Abduction; 6. Semantics of programs with nega- tion; 7. Nonmonotonicity in logic programming.  ...  of filters and ideals on the set-theoretical lattice of truth values).  ... 

Improved Application of Paraconsistent Artificial Neural Networks in Diagnosis of Alzheimer's Disease

Helder F.S. Lopes, Jair M. Abe, Paulo A.M. Kanda, Sergio Machado, Bruna Velasques, Pedro Ribeiro, Luis F.H. Basile, Ricardo Nitrini, Renato Anghinah
2011 Neuroscience International  
Thirty three AD patients and thirty four controls patients of EEG records were obtained during relaxed wakefulness.  ...  for recognizing predetermined patterns of EEG activity and to assess its value as a possible complementary method for AD diagnosis.  ...  In order to manipulate this information directly, recently, some interesting theories have been proposed: fuzzy sets and rough sets for example.  ... 
doi:10.3844/amjnsp.2011.17.27 fatcat:ikqilkxohbabvm5vhu5huulnbe

Improved Application of Paraconsistent Artificial Neural Networks in Diagnosis of Alzheimer's Disease

Lopes
2011 Neuroscience International  
Thirty three AD patients and thirty four controls patients of EEG records were obtained during relaxed wakefulness.  ...  for recognizing predetermined patterns of EEG activity and to assess its value as a possible complementary method for AD diagnosis.  ...  In order to manipulate this information directly, recently, some interesting theories have been proposed: fuzzy sets and rough sets for example.  ... 
doi:10.3844/amjnsp.2011.54.64 fatcat:3t6mexb5uzh4ph5ummwgb2d2fy

Logical Pluralism and Interpretations of Logical Systems

Diego Tajer, Camillo Fiore
2022 Logic and Logical Philosophy  
Carnielli and Rodrigues [2019a] defend an epistemic interpretation of the paraconsistent logic N4, according to which an argument is valid in this logic just in case it necessarily preserves evidence.  ...  We consider four variants of this idea, bring up some possible objections, and try to find plausible solutions on behalf of the pluralist.  ...  So, for another example, Carnielli and Rodrigues [2019a] propose a two-valued non-compositional semantics for the paraconsistent logic N4, where the semantic values '1' and '0' are interpreted as, respectively  ... 
doi:10.12775/llp.2022.007 fatcat:aqysdsq7fbgr5fygcsdw3lu6d4

Dialectical Rough Sets, Parthood and Figures of Opposition-1 [article]

A. Mani
2018 arXiv   pre-print
In this paper dialectical rough logics are invented from a semantic perspective, a concept of dialectical predicates is formalised, connection with dialetheias and glutty negation are established, parthood  ...  In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context  ...  The 4-valued DDT (see Tzouvaras (2001) ) addresses some of these concerns with a justification for 3-valuedness in some semantics of classical RST.  ... 
arXiv:1703.10251v2 fatcat:a25hhwoig5hp7poozapuwayjwu

Paraconsistent logic programming

Howard A. Blair, V.S. Subrahmanian
1989 Theoretical Computer Science  
First, we give a semantics for sets of clauses of the syntactic form L",$= L, & 0304-3975/89/$3.50 0 1989, Elsevier Science Publishers B.V. (North-Holland)  ...  The set Y = {I, t, f, T} is the set of truth values of our four-valued logic.  ...  Logics of this kind are often called paraconsistent logics.  ... 
doi:10.1016/0304-3975(89)90126-6 fatcat:x6cjjdsr75dwbp247lrq7h5vle
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