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Probabilistic Formal Concepts with Negation [chapter]

E. E. Vityaev, V. V. Martinovich
2015 Lecture Notes in Computer Science  
This generalization is obtained from the notion of 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.  ... 
doi:10.1007/978-3-662-46823-4_31 fatcat:ekiynjnweza67komsbx2mkpojq

Recovering Noisy Contexts with Probabilistic Formal Concepts

Vitaliy V. Martynovich, Euvgeniy E. Vityaev
2016 International Conference on Concept Lattices and their Applications  
We developed a 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.  ... 
dblp:conf/cla/Martynovich16 fatcat:p4r3ze5jf5b25fjfmujb4ahxim

Paraconsistent Foundations for Probabilistic Reasoning, Programming and Concept Formation [article]

Ben Goertzel
2021 arXiv   pre-print
via 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.  ... 
arXiv:2012.14474v2 fatcat:4zfsz3taqnbfjayux7zly7w2ia

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].  ... 

Probabilistic Description Logics [article]

Jochen Heinsohn
2013 arXiv   pre-print
We present the 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  ... 
arXiv:1302.6817v1 fatcat:rv2nkiyconfjffq7xmhejzypzm

Providing an Uncertainty Reasoning Service for Semantic Web Application [chapter]

Lei Li, Qiaoling Liu, Yunfeng Tao, Lei Zhang, Jian Zhou, Yong Yu
2006 Lecture Notes in Computer Science  
In the semantic web context,the 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.  ... 
doi:10.1007/11610113_55 fatcat:io76s6ll4faivl5ooo2smkh6vy

Tractable Reasoning with Bayesian Description Logics [chapter]

Claudia d'Amato, Nicola Fanizzi, Thomas Lukasiewicz
2008 Lecture Notes in Computer Science  
For this reason, the new 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.  ... 
doi:10.1007/978-3-540-87993-0_13 fatcat:hjdc2bxdejfypb4r2zyg7yjcsq

Experiments on Aristotle's Thesis

Niki Pfeifer, Sherwood J. B. Sugden
2012 The Monist  
Aristotle's Thesis is a 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.  ... 
doi:10.5840/monist201295213 fatcat:cn3vxuahnzfmhh5tee73k4wotm

Brain Principles Programming [article]

Evgenii Vityaev, Anton Kolonin, Andrey Kurpatov, Artem Molchanov
2022 arXiv   pre-print
This monograph provides a 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.  ... 
arXiv:2202.12710v3 fatcat:vvh6gvrv7bc3ffii5jwkwrj7h4

Animal reasoning and proto-logic [chapter]

José Luis Bermúdez
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 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  ... 
doi:10.1093/acprof:oso/9780198528272.003.0005 fatcat:pteqfnyh6reh3a2b5t7cnjhsei

Quantum Structure in Cognition and the Foundations of Human Reasoning

Diederik Aerts, Sandro Sozzo, Tomas Veloz
2015 International Journal of Theoretical Physics  
Meanwhile, the 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] .  ... 
doi:10.1007/s10773-015-2717-9 fatcat:654ikg3o6badhaav3xyibhibem

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  ... 

Description logic programs under probabilistic uncertainty and fuzzy vagueness

Thomas Lukasiewicz, Umberto Straccia
2009 International Journal of Approximate Reasoning  
More concretely, we present 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).  ... 
doi:10.1016/j.ijar.2009.03.004 fatcat:yycaw6pcjvcz7j6xtqrv54fbqm

Description Logic Programs Under Probabilistic Uncertainty and Fuzzy Vagueness [chapter]

Thomas Lukasiewicz, Umberto Straccia
2007 Lecture Notes in Computer Science  
More concretely, we present 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).  ... 
doi:10.1007/978-3-540-75256-1_19 fatcat:5d3l2xuh5zdf3h4adltf6y4tjq

Probabilistic Concepts in Formal Contexts [chapter]

Alexander Demin, Denis Ponomaryov, Evgeny Vityaev
2012 Lecture Notes in Computer Science  
We generalize the main notions of 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.  ... 
doi:10.1007/978-3-642-29709-0_33 fatcat:d2yw4wpc7zhbjd6mkdasi7rfry
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