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A logical approach to interpolation based on similarity relations

Didier Dubois, Henri Prade, Francesc Esteva, Pere Garcia, Lluís Godo
1997 International Journal of Approximate Reasoning  
In this paper, we investigate how a logic of similarity dedicated to interpolation can be defined, by considering different natural consequence relations induced by the presence of a similarity relation  ...  Our approach strikingly differs from the logics of indiscernibility, such as the rough-set logics, because emphasis is put on interpolation capabilities.  ...  ACKNOWLEDGMENTS The authors have been supported by the joint CSIC-CNRS project "Similarity-based Reasoning and Applications."  ... 
doi:10.1016/s0888-613x(96)00137-5 fatcat:mfxt6xjvz5bt3fyr23373pjesu

Page 7308 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
We explore a modal approach to similarity-based reasoning, and we define three multi-modal systems with similarity-based Kripke model semantics.  ...  In this paper, we investigate how a logic of similarity dedicated to interpolation can be defined, by consider- ing various natural consequence relations induced by the presence of a similarity relation  ... 

Formalization of Human Categorization Process Using Interpolative Boolean Algebra

Vladimir Dobrić, Darko Kovačević, Bratislav Petrović, Dragan Radojević, Pavle Milošević
2015 Mathematical Problems in Engineering  
In this paper, the prototype theory is approached by using structure-functional fuzzy logic, the interpolative Boolean algebra. The proposed formalism is within the Boolean frame.  ...  Approaching the prototype theory by using truth-functional fuzzy logic has been harshly criticized due to not satisfying the complementation laws.  ...  In opposition to conventional fuzzy logics, this approach is based on the fundamental principle of structure functionality.  ... 
doi:10.1155/2015/620797 fatcat:6m5b2rdvqzemnliwf43wm3hguy

Page 5951 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
Introduction: “This general approach to counterfactuals—which appeals to similarity relations between possible worlds—was first set out by Robert Stalnaker [Studies in logical theory: Ameri- can Philosophical  ...  Extended Gentzen-type formulations of two temporal logics based on incomplete knowledge systems.  ... 

A Consensus Model in Group Decision Making Based on Interpolative Boolean Algebra

Ana Poledica, Pavle Milosevic, Ivana Dragovic, Dragan Radojevic, Bratislav Petrovic
2013 Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology  
The aim of this paper is to propose a soft consensus model based on interpolative Boolean algebra for group decision making problems.  ...  The relation of equivalence is employed as a similarity measure among experts' opinions. In fact real-valued realization of equivalence is used as a generalized Boolean polynomial.  ...  In order to determine a level of agreement among experts, IBA equivalence is employed as a logic-based similarity measure.  ... 
doi:10.2991/eusflat.2013.98 dblp:conf/eusflat/PoledicaMDRP13 fatcat:5xeowc5evbfavgo5ypktai4gfe

Fuzzy Control for Knowledge-Based Interpolation [chapter]

Christian Moewes, Rudolf Kruse
2012 Studies in Fuzziness and Soft Computing  
It can be seen as knowledge-based interpolation based on input-output points of a vaguely known function.  ...  Fuzzy control accounts for the biggest industrial success of fuzzy logic. We review an interpretation of Mamdani's heuristic control approach.  ...  The idle speed controller is based on similarity relations (see Section 3). This helps to view the control function as interpolation of a point-wise known function.  ... 
doi:10.1007/978-3-642-24666-1_7 fatcat:oab6rvp5yrezpcuomoptgtd5pe

What does fuzzy logic bring to AI?

Didier Dubois, Henri Prade
1995 ACM Computing Surveys  
FOR FURTHER READING DCTBORS, D., ESTEV& F , GARCIA, P., Go~o, L , AND PRADE, H. 1995 Similarity-based conse- quence relations In Symbolic and Quantltatme Approaches to Reasorung and Uncertainty  ...  Connections with other approaches to nonmonotonic reasoning, including one based on in- finitesimal probabilities, have been laid bare.  ... 
doi:10.1145/212094.212115 fatcat:yjfii6oc3rc4jlnem24odgdxci

Quantifier Elimination via Functional Composition [chapter]

Jie-Hong R. Jiang
2009 Lecture Notes in Computer Science  
Its answer leads to a solution to quantifier elimination in the Boolean domain, alternative to the conventional approach based on formula expansion.  ...  This compositional approach to quantifier elimination is analyzably superior to the conventional one under certain practical assumptions. Experiments demonstrate the scalability of the approach.  ...  On the other hand, recent progress in AIG packages [14, 13] has made AIG-based quantification a viable alternative to BDD-based one.  ... 
doi:10.1007/978-3-642-02658-4_30 fatcat:ptyq7dsppjcy3iijjfsxt3olni

Page 8176 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
A range of different semantics (based on the least fixed points of a monotone operator) for default logic is presented as an alternative approach to Reiter’s original semantics.  ...  {Reviewer’s remarks: A closely related tableau system which axiomatizes distinct (but similar) paraconsistent logics was in- troduced by the reviewer and M. Lima-Marques [J. Appl.  ... 

Interpolation in Equilibrium Logic and Answer Set Programming: the Propositional Case [article]

Dov Gabbay and David Pearce and Agustí n Valverde
2010 arXiv   pre-print
For disjunctive logic programs we also study the property of uniform interpolation that is closely related to the concept of variable forgetting.  ...  These results also yield a form of interpolation for ground logic programs under the answer sets semantics.  ...  To express the idea that a formula is an interpolant one approach is simply to replace ⊢ by | ∼ in (1). We may call this form (| ∼, | ∼)-interpolation.  ... 
arXiv:1012.3947v1 fatcat:2rjgcxtlafbjvimtlysxcaaehq

Reformulating Queries: Theory and Practice

Michael Benedikt, Egor V. Kostylev, Fabio Mogavero, Efthymia Tsamoura
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
We consider a setting where a user wants to pose a query against a dataset where background knowledge, expressed as logical sentences, is available, but only a subset of the information can be used to  ...  We thus want to reformulate the user query against the subvocabulary, arriving at a query equivalent to the user's query assuming the background theory, but using only the restricted vocabulary.  ...  The first approach is based on an interpolation module native to a prover, which is used as a "black box" to get reformulations.  ... 
doi:10.24963/ijcai.2017/116 dblp:conf/ijcai/BenediktKMT17 fatcat:k7jrrwnglvfrfb2hli673ubqxm

A Knowledge Level Account of Forgetting

James P. Delgrande
2017 The Journal of Artificial Intelligence Research  
Foremost, it provides a uniform approach to forgetting, with a definition that is applicable to any logic with a well-defined consequence relation.  ...  Forgetting is an operation on knowledge bases that has been addressed in different areas of Knowledge Representation and with respect to different formalisms, including classical propositional and first-order  ...  I thank a second reviewer for helpful comments, particularly with regards to work in answer set programmming.  ... 
doi:10.1613/jair.5530 fatcat:wvidqe2ukfbodkhuzssikq4upy

IBA-based framework for modeling similarity

Pavle Milosević, Ana Poledica, Aleksandar Rakićević, Vladimir Dobrić, Bratislav Petrović, Dragan Radojević
2018 International Journal of Computational Intelligence Systems  
In this paper, we introduce a logic-driven framework for modeling similarity based on interpolative Boolean algebra (IBA).  ...  Furthermore, the example of similarity-based classification demonstrates the descriptive power and transparency of the framework on real financial data.  ...  In this paper, we present a novel logic-driven framework for modeling similarity between multiattribute objects based on interpolative Boolean algebra (IBA).  ... 
doi:10.2991/ijcis.11.1.16 fatcat:4oytzdnipvfppl7pzlf7sskvpq

An Automated System for Stock Market Trading Based on Logical Clustering

2018 Tehnički Vjesnik  
It relies on interpolative Boolean algebra as underlying mathematical framework used to construct logical clustering method which is the central component of the system.  ...  Finally, a simple trading simulation engine is developed to test our system on real market data.  ...  In LC approach, dissimilarity between objects is measured using an interpolative relation of exclusive disjunction, which is a logical function with [0,1] value realization based on IBA.  ... 
doi:10.17559/tv-20160318145514 fatcat:7qnm7lo2bzgprj4w4du2ntc2gu

Guiding Craig interpolation with domain-specific abstractions

Jérôme Leroux, Philipp Rümmer, Pavle Subotić
2015 Acta Informatica  
We present a semantic and solver-independent framework for systematically exploring interpolant lattices, based on the notion of interpolation abstraction.  ...  One of the most common methods to construct or refine abstractions is Craig interpolation [15], a logical tool to extract concise explanations for the (bounded) unreachability of error locations or states  ...  , leading to a similar formula i 2 ≤ 2, and so on.  ... 
doi:10.1007/s00236-015-0236-z fatcat:3lcbb2vllbhljcajdbto6ghvqm
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