133,015 research outputs found
Elimination of Cuts in First-order Finite-valued Logics
A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information
Temporal Query Answering in DL-Lite over Inconsistent Data
In ontology-based systems that process data stemming from different sources and that is received over time, as in context-aware systems, reasoning needs to cope with the temporal dimension and should be resilient against inconsistencies in the data. Motivated by such settings, this paper addresses the problem of handling inconsistent data in a temporal version of ontology-based query answering. We consider a recently proposed temporal query language that combines conjunctive queries with operators of propositional linear temporal logic and extend to this setting three inconsistency-tolerant semantics that have been introduced for querying inconsistent description logic knowledge bases. We investigate their complexity for DL-LiteR temporal knowledge bases, and furthermore complete the picture for the consistent case
Propositional Non-Monotonic Reasoning and Inconsistency in Symmetric Neural Networks
We define a notion of reasoning using world-rank-functions, independently of any symbolic language. We then show that every symmetric neural network (like Hopfield networks or Boltzman machines) can be seen as performing a search for a satisfying model of some knowledge that is wired into the network\u27s topology and weights. Several equivalent languages are then shown to describe symbolically the knowledge embedded in these networks. We extend propositional calculus by augmenting assumptions with penalties. The extended calculus (called penalty logic ) is useful in expressing default knowledge, preference between arguments, and reliability of assumptions in an inconsistent knowledge base. Every symmetric network can be described by this language and any sentence in the language is translatable to such network. A proof-theoretic reasoning procedure supplements the model-theoretic definitions and gives an intuitive understanding of the non-monotonic behavior of the reasoning mechanism. Finally we sketch a connectionist inference engine for penalty logic and discuss its capabilities and limitations
A Neutrosophic Description Logic
Description Logics (DLs) are appropriate, widely used, logics for managing
structured knowledge. They allow reasoning about individuals and concepts, i.e.
set of individuals with common properties. Typically, DLs are limited to
dealing with crisp, well defined concepts. That is, concepts for which the
problem whether an individual is an instance of it is yes/no question. More
often than not, the concepts encountered in the real world do not have a
precisely defined criteria of membership: we may say that an individual is an
instance of a concept only to a certain degree, depending on the individual's
properties. The DLs that deal with such fuzzy concepts are called fuzzy DLs. In
order to deal with fuzzy, incomplete, indeterminate and inconsistent concepts,
we need to extend the fuzzy DLs, combining the neutrosophic logic with a
classical DL. In particular, concepts become neutrosophic (here neutrosophic
means fuzzy, incomplete, indeterminate, and inconsistent), thus reasoning about
neutrosophic concepts is supported. We'll define its syntax, its semantics, and
describe its properties.Comment: 18 pages. Presented at the IEEE International Conference on Granular
Computing, Georgia State University, Atlanta, USA, May 200
Neuro-Symbolic Recommendation Model based on Logic Query
A recommendation system assists users in finding items that are relevant to
them. Existing recommendation models are primarily based on predicting
relationships between users and items and use complex matching models or
incorporate extensive external information to capture association patterns in
data. However, recommendation is not only a problem of inductive statistics
using data; it is also a cognitive task of reasoning decisions based on
knowledge extracted from information. Hence, a logic system could naturally be
incorporated for the reasoning in a recommendation task. However, although
hard-rule approaches based on logic systems can provide powerful reasoning
ability, they struggle to cope with inconsistent and incomplete knowledge in
real-world tasks, especially for complex tasks such as recommendation.
Therefore, in this paper, we propose a neuro-symbolic recommendation model,
which transforms the user history interactions into a logic expression and then
transforms the recommendation prediction into a query task based on this logic
expression. The logic expressions are then computed based on the modular logic
operations of the neural network. We also construct an implicit logic encoder
to reasonably reduce the complexity of the logic computation. Finally, a user's
interest items can be queried in the vector space based on the computation
results. Experiments on three well-known datasets verified that our method
performs better compared to state of the art shallow, deep, session, and
reasoning models.Comment: 17 pages, 6 figure
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