An interesting feature that traditional approaches to inductive logicprogramming are missing is the ability to treat noisy and non-logical data. Neural-symbolic approaches to inductive logicprogramming have been rec...
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ISBN:
(纸本)9783031157073;9783031157066
An interesting feature that traditional approaches to inductive logicprogramming are missing is the ability to treat noisy and non-logical data. Neural-symbolic approaches to inductive logicprogramming have been recently proposed to combine the advantages of inductive logicprogramming, in terms of interpretability and generalization capability, withthe characteristic capacity of deep learning to treat noisy and nonlogical data. this paper concisely surveys and briefly compares three promising neural-symbolic approaches to inductive logicprogrammingthat have been proposed in the last five years. the considered approaches use Datalog dialects to represent background knowledge, and they are capable of producing reusable logical rules from noisy and non-logical data. therefore, they provide an effective means to combine logical reasoning with state-of-the-art machine learning.
Induction proofs often fail because the stated theorem is noninductive, in which case the user must strengthen the theorem or prove auxiliary properties before performing the induction step. (Counter)model finders are...
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ISBN:
(纸本)9783642162411
Induction proofs often fail because the stated theorem is noninductive, in which case the user must strengthen the theorem or prove auxiliary properties before performing the induction step. (Counter)model finders are useful for detecting non-theorems, but they will not find any counterexamples for noninductive theorems. We explain how to apply a well-known concept from first-order logic, nonstandard models, to the detection of noninductive invariants. Our work was done in the context of the proof assistant Isabelle/HOL and the counterexample generator Nitpick.
Uncertain information is present in many real applications e.g., medical domain, weather forecast, etc. the most common approaches for leading withthis information are based on probability however some times;it is di...
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ISBN:
(纸本)9783540766308
Uncertain information is present in many real applications e.g., medical domain, weather forecast, etc. the most common approaches for leading withthis information are based on probability however some times;it is difficult to find suitable probabilities about some events. In this paper, we present a possibilistic logicprogramming approach which is based on possibilistic logic and PStable semantics. Possibilistic logic is a logic of uncertainty tailored for reasoning under incomplete evidence and Pstable Semantics is a solid semantics which emerges from the fusion of non-monotonicreasoning and logicprogramming;moreover it is able to express answer set semantics, and has strong connections with paraconsistent logics.
Axiom pinpointing is the task of identifying the axiomatic causes for a consequence to follow from an ontology. Different approaches have been proposed in the literature for finding one or all the subset-minimal subon...
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ISBN:
(纸本)9783031157073;9783031157066
Axiom pinpointing is the task of identifying the axiomatic causes for a consequence to follow from an ontology. Different approaches have been proposed in the literature for finding one or all the subset-minimal subontologies that preserve a description logic consequence. We propose an approach that leverages the capabilities of answer set programming for transparent axiom pinpointing. We show how other associated tasks can be modelled without much additional effort.
the proceedings contain 94 papers. the topics discussed include: inputs, outputs, and composition in the logic of information flows;reasoning with contextual knowledge and influence diagrams;verifying strategic abilit...
ISBN:
(纸本)9781713825982
the proceedings contain 94 papers. the topics discussed include: inputs, outputs, and composition in the logic of information flows;reasoning with contextual knowledge and influence diagrams;verifying strategic abilities of neural-symbolic multi-agent systems;explainable acceptance in probabilistic abstract argumentation: complexity and approximation;answer set programming with composed predicate names;symbolic solutions for symbolic constraint satisfaction problems;an answer set programming framework for reasoning about agents' beliefs and truthfulness of statements;syntax splitting for iterated contractions;reasoning with inconsistent knowledge using the epistemic approach to probabilistic argumentation;plausible reasoning about el-ontologies using concept interpolation;and on the decidability of expressive description logics with transitive closure and regular role expressions.
In this paper we study the problem of concept contraction for the description logic EL. Concept contraction is concerned withthe following question: Given two concepts C and D (withthe interesting case being that D ...
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ISBN:
(纸本)9780999241172
In this paper we study the problem of concept contraction for the description logic EL. Concept contraction is concerned withthe following question: Given two concepts C and D (withthe interesting case being that D subsumes C) how can we find a generalisation of C that is not subsumed by D but is otherwise as similar as possible to C? We take an AGM-style approach and model this problem using the notion of a concept contraction operator. We consider constructive definitions as well as sets of postulates for concept contraction, and link the two by means of representation theorems.
Influence diagrams (IDs) are well-known formalisms extending Bayesian networks to model decision situations under uncertainty. Although they are convenient as a decision theoretic tool, their knowledge representation ...
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ISBN:
(纸本)9780999241172
Influence diagrams (IDs) are well-known formalisms extending Bayesian networks to model decision situations under uncertainty. Although they are convenient as a decision theoretic tool, their knowledge representation ability is limited in capturing other crucial notions such as logical consistency. We complement IDs withthe light-weight description logic (DL) EL to overcome such limitations. We consider a setup where DL axioms hold in some contexts, yet the actual context is uncertain. the framework benefits from the convenience of using DL as a domain knowledge representation language and the modelling strength of IDs to deal with decisions over contexts in the presence of contextual uncertainty. We define related reasoning problems and study their computational complexity.
Justification theory is a unifying semantic framework. While it has its roots in non-monotoniclogics, it can be applied to various areas in computer science, especially in explainable reasoning;its most central conce...
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Justification theory is a unifying semantic framework. While it has its roots in non-monotoniclogics, it can be applied to various areas in computer science, especially in explainable reasoning;its most central concept is a justification: an explanation why a property holds (or does not hold) in a model. In this paper, we continue the study of justification theory by means of three major contributions. the first is studying the relation between justification theory and game theory. We show that justification frameworks can be seen as a special type of games. the established connection provides the theoretical foundations for our next two contributions. the second contribution is studying under which condition two different dialects of justification theory (graphs as explanations vs trees as explanations) coincide. the third contribution is establishing a precise criterion of when a semantics induced by justification theory yields consistent results. In the past proving that such semantics were consistent took cumbersome and elaborate proofs. We show that these criteria are indeed satisfied for all common semantics of logicprogramming.
the proceedings contain 94 papers. the topics discussed include: inputs, outputs, and composition in the logic of information flows;reasoning with contextual knowledge and influence diagrams;verifying strategic abilit...
ISBN:
(纸本)9781713825982
the proceedings contain 94 papers. the topics discussed include: inputs, outputs, and composition in the logic of information flows;reasoning with contextual knowledge and influence diagrams;verifying strategic abilities of neural-symbolic multi-agent systems;explainable acceptance in probabilistic abstract argumentation: complexity and approximation;answer set programming with composed predicate names;symbolic solutions for symbolic constraint satisfaction problems;an answer set programming framework for reasoning about agents' beliefs and truthfulness of statements;syntax splitting for iterated contractions;reasoning with inconsistent knowledge using the epistemic approach to probabilistic argumentation;plausible reasoning about el-ontologies using concept interpolation;and on the decidability of expressive description logics with transitive closure and regular role expressions.
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