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A logical approach to interpolation based on similarity relations
1997
International Journal of Approximate Reasoning
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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
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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
2015
Mathematical Problems in Engineering
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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
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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
2013
Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology
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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]
2012
Studies in Fuzziness and Soft Computing
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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?
1995
ACM Computing Surveys
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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]
2009
Lecture Notes in Computer Science
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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
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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]
2010
arXiv
pre-print
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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
2017
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
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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
2017
The Journal of Artificial Intelligence Research
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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
2018
International Journal of Computational Intelligence Systems
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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
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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
2015
Acta Informatica
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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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