27,859 research outputs found
Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories
The computer-mechanization of an ambitious explicit ethical theory, Gewirth's
Principle of Generic Consistency, is used to showcase an approach for
representing and reasoning with ethical theories exhibiting complex logical
features like alethic and deontic modalities, indexicals, higher-order
quantification, among others. Harnessing the high expressive power of Church's
type theory as a meta-logic to semantically embed a combination of quantified
non-classical logics, our work pushes existing boundaries in knowledge
representation and reasoning. We demonstrate that intuitive encodings of
complex ethical theories and their automation on the computer are no longer
antipodes.Comment: 14 page
The Grand Challenges and Myths of Neural-Symbolic Computation
The construction of computational cognitive models integrating the connectionist and symbolic paradigms of artificial intelligence is a standing research issue in the field. The combination of logic-based inference and connectionist learning systems may lead to the construction of semantically sound computational cognitive models in artificial intelligence, computer and cognitive sciences. Over the last decades, results regarding the computation and learning of classical reasoning within neural networks have been promising. Nonetheless, there still remains much do be done. Artificial intelligence, cognitive and computer science are strongly based on several non-classical reasoning formalisms, methodologies and logics. In knowledge representation, distributed systems, hardware design, theorem proving, systems specification and verification classical and non-classical logics have had a great impact on theory and real-world applications. Several challenges for neural-symbolic computation are pointed out, in particular for classical and non-classical computation in connectionist systems. We also analyse myths about neural-symbolic computation and shed new light on them considering recent research advances
Non classical concept representation and reasoning in formal ontologies
Formal ontologies are nowadays widely considered a standard tool for knowledge
representation and reasoning in the Semantic Web. In this context, they are expected to
play an important role in helping automated processes to access information. Namely:
they are expected to provide a formal structure able to explicate the relationships
between different concepts/terms, thus allowing intelligent agents to interpret, correctly,
the semantics of the web resources improving the performances of the search
technologies.
Here we take into account a problem regarding Knowledge Representation in general,
and ontology based representations in particular; namely: the fact that knowledge
modeling seems to be constrained between conflicting requirements, such as
compositionality, on the one hand and the need to represent prototypical information on
the other. In particular, most common sense concepts seem not to be captured by the
stringent semantics expressed by such formalisms as, for example, Description Logics
(which are the formalisms on which the ontology languages have been built). The aim
of this work is to analyse this problem, suggesting a possible solution suitable for
formal ontologies and semantic web representations.
The questions guiding this research, in fact, have been: is it possible to provide a formal
representational framework which, for the same concept, combines both the classical
modelling view (accounting for compositional information) and defeasible, prototypical
knowledge ? Is it possible to propose a modelling architecture able to provide different
type of reasoning (e.g. classical deductive reasoning for the compositional component
and a non monotonic reasoning for the prototypical one)?
We suggest a possible answer to these questions proposing a modelling framework able
to represent, within the semantic web languages, a multilevel representation of
conceptual information, integrating both classical and non classical (typicality based)
information. Within this framework we hypothesise, at least in principle, the coexistence of multiple reasoning processes involving the different levels of
representation
Principles of KLM-style Defeasible Description Logics
The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition.
We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferen- tial and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our seman- tics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC
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