501 research outputs found
A Description Logic Framework for Commonsense Conceptual Combination Integrating Typicality, Probabilities and Cognitive Heuristics
We propose a nonmonotonic Description Logic of typicality able to account for
the phenomenon of concept combination of prototypical concepts. The proposed
logic relies on the logic of typicality ALC TR, whose semantics is based on the
notion of rational closure, as well as on the distributed semantics of
probabilistic Description Logics, and is equipped with a cognitive heuristic
used by humans for concept composition. We first extend the logic of typicality
ALC TR by typicality inclusions whose intuitive meaning is that "there is
probability p about the fact that typical Cs are Ds". As in the distributed
semantics, we define different scenarios containing only some typicality
inclusions, each one having a suitable probability. We then focus on those
scenarios whose probabilities belong to a given and fixed range, and we exploit
such scenarios in order to ascribe typical properties to a concept C obtained
as the combination of two prototypical concepts. We also show that reasoning in
the proposed Description Logic is EXPTIME-complete as for the underlying ALC.Comment: 39 pages, 3 figure
Beyond subgoaling: A dynamic knowledge generation framework for creative problem solving in cognitive architectures
In this paper we propose a computational framework aimed at extending the problem solving capabilities of cognitive artificial agents through the introduction of a novel, goal-directed, dynamic knowledge generation mechanism obtained via a non monotonic reasoning procedure. In particular, the proposed framework relies on the assumption that certain classes of problems cannot be solved by simply learning or injecting new external knowledge in the declarative memory of a cognitive artificial agent but, on the other hand, require a mechanism for the automatic and creative re-framing, or re-formulation, of the available knowledge. We show how such mechanism can be obtained trough a framework of dynamic knowledge generation that is able to tackle the problem of commonsense concept combination. In addition, we show how such a framework can be employed in the field of cognitive architectures in order to overcome
situations like the impasse in SOAR by extending the possible options of its subgoaling procedures
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
A connection method for a defeasible extension of
This paper proposes a connection method \`a la Bibel for an
exception-tolerant family of description logics (DLs). As for the language, we
assume the DL extended with two typicality operators: one on
(complex) concepts and one on role names. The language is a variant of
defeasible DLs, as broadly studied in the literature over the past decade, in
which most of these can be embedded. We revisit the definition of the matrix
representation of a knowledge base and establish the conditions for a given
axiom to be provable. We show that the calculus terminates and is sound and
complete w.r.t. a DL version of the preferential semantics widely adopted in
non-monotonic reasoning
Representing Concepts by Weighted Formulas
A concept is traditionally defined via the necessary and sufficient conditions
that clearly determine its extension. By contrast, cognitive views of concepts
intend to account for empirical data that show that categorisation under a concept
presents typicality effects and a certain degree of indeterminacy. We propose a formal
language to compactly represent concepts by leveraging on weighted logical
formulas. In this way, we can model the possible synergies among the qualities that
are relevant for categorising an object under a concept. We show that our proposal
can account for a number of views of concepts such as the prototype theory and the
exemplar theory. Moreover, we show how the proposed model can overcome some
limitations of cognitive views
A KLM Perspective on Defeasible Reasoning for Description Logics
In this paper we present an approach to defeasible reasoning for the description logic ALC. The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case. We consider versions of a preferential semantics for two forms of defeasible subsumption, and link these semantic constructions formally to KLM-style syntactic properties via representation results. In addition to showing that the semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. With the semantics of the defeasible version of ALC in place, we turn to the investigation of an appropriate form of defeasible entailment for this enriched version of ALC. This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case. Importantly, the algorithm relies completely on classical entailment checks and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of the underlying classical ALC. Before concluding, we take a brief tour of some existing work on defeasible extensions of ALC that go beyond defeasible subsumption
A Toothful of Concepts: Towards a Theory of Weighted Concept Combination
We introduce a family of operators to combine Description
Logic concepts. They aim to characterise complex concepts that apply
to instances that satisfy \enough" of the concept descriptions given. For
instance, an individual might not have any tusks, but still be considered
an elephant. To formalise the meaning of "enough", the operators take a
list of weighted concepts as arguments, and a certain threshold to be met.
We commence a study of the formal properties of these operators, and
study some variations. The intended applications concern the representation
of cognitive aspects of classication tasks: the interdependencies
among the attributes that dene a concept, the prototype of a concept,
and the typicality of the instances
A Description Logic Framework for Commonsense Conceptual Combination Integrating Typicality, Probabilities and Cognitive Heuristics
We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of the combination of prototypical concepts. The proposed logic relies on the logic
of typicality ALC + TR, whose semantics is based on the notion of rational closure, as well
as on the distributed semantics of probabilistic Description Logics, and is equipped with a
cognitive heuristic used by humans for concept composition.
We first extend the logic of typicality ALC + TR by typicality inclusions of the form
p :: T(C) v D, whose intuitive meaning is that “we believe with degree p about the fact that
typical Cs are Ds”. As in the distributed semantics, we define different scenarios containing
only some typicality inclusions, each one having a suitable probability. We then exploit such
scenarios in order to ascribe typical properties to a concept C obtained as the combination of
two prototypical concepts. We also show that reasoning in the proposed Description Logic is
EXPTIME-complete as for the underlying standard Description Logic ALC
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