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Probabilistic Formal Concepts with Negation
[chapter]

2015
*
Lecture Notes in Computer Science
*

This generalization is obtained from the notion of

doi:10.1007/978-3-662-46823-4_31
fatcat:ekiynjnweza67komsbx2mkpojq
*formal**concepts**with*its definition as fixed points of implications, when implications, possibly*with**negations*, are replaced by*probabilistic*laws. ... In the end, the demonstration for the*probabilistic**formal**concepts*formation is given together*with*noise resistance example. ... Here we introduce the*probabilistic*generalization of the*formal**concepts**with**negations*for many-valued contexts. ...##
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Recovering Noisy Contexts with Probabilistic Formal Concepts

2016
*
International Conference on Concept Lattices and their Applications
*

We developed a

dblp:conf/cla/Martynovich16
fatcat:p4r3ze5jf5b25fjfmujb4ahxim
*probabilistic*generalization of*formal**concepts*which seems to avoid a monstrous combinatorial complexity of a complete context lattice construction. ... We managed to bypass the filtering problem by applying a sort of*probabilistic*approach. ... The next step is to equip*concepts**with*possible attribute*negations*and develop a logical language of a context*probabilistic*reasoning. ...##
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Paraconsistent Foundations for Probabilistic Reasoning, Programming and Concept Formation
[article]

2021
*
arXiv
*
pre-print

via

arXiv:2012.14474v2
fatcat:4zfsz3taqnbfjayux7zly7w2ia
*Formal**Concept*Analysis is presented, building on a definition of fuzzy property-value degrees in terms of relative entropy on paraconsistent probability distributions. ... First it is shown that appropriate averaging-across-situations and renormalization of 4-valued p-bits operating in accordance*with*Constructible Duality (CD) logic yields PLN (*Probabilistic*Logic Networks ... A fuzzy*formal**concept*is then a pair where O ! = P and P ! = O. ...##
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Page 6714 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

In particular, we show that the notions of g-coherence and of g- coherent entailment can be expressed by combining notions in model-theoretic

*probabilistic*logic*with**concepts*from default rea- soning. ... The approach is based on a symmetry of involutive*negations**with*respect to the line f(x) =x, x € [0, 1]. ...##
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Probabilistic Description Logics
[article]

2013
*
arXiv
*
pre-print

We present the

arXiv:1302.6817v1
fatcat:rv2nkiyconfjffq7xmhejzypzm
*formal*semantics underlying the language ALUP and introduce the*probabilistic**formalism*that is based on classes of probabilities and is realized by means of*probabilistic*constraints. ... On the one hand, classical terminological knowledge representation excludes the possibility of handling uncertain*concept*descriptions involving, e.g., "usually true"*concept*properties, generalized quantifiers ... disjunction*concept**negation*value restriction existential restriction*With*an introduction to*formal*semantics of ACC in mind, we give a translation into set theoretical expres sions*with*1> being the ...##
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Providing an Uncertainty Reasoning Service for Semantic Web Application
[chapter]

2006
*
Lecture Notes in Computer Science
*

In the semantic web context,the

doi:10.1007/11610113_55
fatcat:io76s6ll4faivl5ooo2smkh6vy
*formal*representation of knowledge is not resourceful while the informal one*with*uncertainty prevails. ... In order to provide an uncertainty reasoning service for semantic web applications, we propose a*probabilistic*extension of Description Logic, namely*Probabilistic*Description Logic Program (PDLP). ... Here,*negation*is allowed on primitive*concepts*rather than arbitrary ones to meet the translating restriction from DL to LP because LP cannot represent arbitrary*negation*. ...##
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Tractable Reasoning with Bayesian Description Logics
[chapter]

2008
*
Lecture Notes in Computer Science
*

For this reason, the new

doi:10.1007/978-3-540-87993-0_13
fatcat:hjdc2bxdejfypb4r2zyg7yjcsq
*probabilistic*description logics are very promising*formalisms*for data-intensive applications in the Semantic Web involving*probabilistic*uncertainty. ... As an important feature, the new*probabilistic*description logics allow for flexibly combining terminological and assertional pieces of*probabilistic*knowledge. ...*Concepts*(in DL-Lite) are defined as follows. Every basic*concept*B and*negation*of a basic*concept*¬B is a*concept*. ...##
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Experiments on Aristotle's Thesis

2012
*
The Monist
*

Aristotle's Thesis is a

doi:10.5840/monist201295213
fatcat:cn3vxuahnzfmhh5tee73k4wotm
*negated*conditional, which consists of one propositional variable*with*a*negation*either in the antecedent (version 1) or in the consequent (version 2). ... Moreover, the second experiment rules out scope ambiguities of the*negation*of conditionals. ... Psychology students and students*with*a*formal*background were not included in the sample. The participants received 5 ¤ for participation. ...##
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Brain Principles Programming
[article]

2022
*
arXiv
*
pre-print

This monograph provides a

arXiv:2202.12710v3
fatcat:vvh6gvrv7bc3ffii5jwkwrj7h4
*formalization*of these principles in terms of the category theory. However, this*formalization*is not enough to develop algorithms for working*with*information. ... As an anthropomorphic direction of research, it considers Brain Principles Programming, BPP) the*formalization*of universal mechanisms (principles) of the brain's work*with*information, which are implemented ... Therefore, statistical approximation of*probabilistic**formal**concepts*is a direct generalization of the original*probabilistic**formal**concepts*in the case of working*with*noisy data. ...##
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Animal reasoning and proto-logic
[chapter]

2006
*
Rational Animals?
*

It explores non-linguistic analogs of basic patterns of inference that can be understood at the linguistic level in terms of rules of inference involving elementary logical

doi:10.1093/acprof:oso/9780198528272.003.0005
fatcat:pteqfnyh6reh3a2b5t7cnjhsei
*concepts*. ... reasoning from an excluded alternative and two types of conditional reasoning) are highly relevant to animal practical reasoning, and I show how animals might apply them without deploying any logical*concepts*... I am fully in agreement*with*apparent example of*probabilistic*(or indeterministic) causation at the macrolevel can be explained in terms of hidden variables, so that what looks like a*probabilistic*...##
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Quantum Structure in Cognition and the Foundations of Human Reasoning

2015
*
International Journal of Theoretical Physics
*

Meanwhile, the

doi:10.1007/s10773-015-2717-9
fatcat:654ikg3o6badhaav3xyibhibem
*formalism*of quantum theory has provided an efficient resource for modeling these classically problematical situations. ... In this paper, we start from our successful quantum-theoretic approach to the modeling of*concept*combinations to formulate a unifying explanatory hypothesis. ... Extending Fock space modeling to conceptual*negation*The first studies on the*negation*of natural*concepts*were also performed by Hampton [9] . ...##
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Page 5107 of Mathematical Reviews Vol. , Issue 93i
[page]

1993
*
Mathematical Reviews
*

Two

*concepts*of*negation*in disjunctive logic programs are proposed in Chapters 5 and 6. ... Summary: “This paper discusses certain issues connected*with*the*formalization*of reasoning; the possibility of*formalization*of certain taxonomical inferences (exceptions) by means of linear connectives ...##
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Description logic programs under probabilistic uncertainty and fuzzy vagueness

2009
*
International Journal of Approximate Reasoning
*

More concretely, we present

doi:10.1016/j.ijar.2009.03.004
fatcat:yycaw6pcjvcz7j6xtqrv54fbqm
*probabilistic*fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (*with*stratified default-*negation*), and*probabilistic*uncertainty ... We define important*concepts*dealing*with*both*probabilistic*uncertainty and fuzzy vagueness, such as the expected truth value of a crisp sentence and the probability of a vague sentence. ... vagueness (in query matching*with*vague*concepts*). ...##
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Description Logic Programs Under Probabilistic Uncertainty and Fuzzy Vagueness
[chapter]

2007
*
Lecture Notes in Computer Science
*

More concretely, we present

doi:10.1007/978-3-540-75256-1_19
fatcat:5d3l2xuh5zdf3h4adltf6y4tjq
*probabilistic*fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (*with*stratified default-*negation*), and*probabilistic*uncertainty ... We define important*concepts*dealing*with*both*probabilistic*uncertainty and fuzzy vagueness, such as the expected truth value of a crisp sentence and the probability of a vague sentence. ... vagueness (in query matching*with*vague*concepts*). ...##
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Probabilistic Concepts in Formal Contexts
[chapter]

2012
*
Lecture Notes in Computer Science
*

We generalize the main notions of

doi:10.1007/978-3-642-29709-0_33
fatcat:d2yw4wpc7zhbjd6mkdasi7rfry
*Formal**Concept*Analysis*with*the ideas of the semantic*probabilistic*inference. ... From the point of view of applications, we propose a method of recovering*concepts*in*formal*contexts in presence of noise on data. ... This is because the*negation*was not present in the fundamentals of*Formal**Concept*Analysis and we aimed at giving the most simple generalization of the basic notions of this method. ...
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