6 research outputs found
Understanding Predication in Conceptual Spaces
We argue that a cognitive semantics has to take into account the possibly
partial information that a cognitive agent has of the world. After discussing
GĂ€rdenfors's view of objects in conceptual spaces, we offer a number of viable
treatments of partiality of information and we formalize them by means of alternative
predicative logics. Our analysis shows that understanding the nature of simple
predicative sentences is crucial for a cognitive semantics
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 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
Towards a Cognitive Semantics of Type
Types are a crucial concept in conceptual modelling, logic, and knowledge representation as they are an ubiquitous device to un- derstand and formalise the classification of objects. We propose a logical treatment of types based on a cognitively inspired modelling that ac- counts for the amount of information that is actually available to a cer- tain agent in the task of classification. We develop a predicative modal logic whose semantics is based on conceptual spaces that model the ac- tual information that a cognitive agent has about objects, types, and the classification of an object under a certain type. In particular, we ac- count for possible failures in the classification, for the lack of sufficient information, and for some aspects related to vagueness
Pink panthers and toothless tigers: three problems in classification
Many aspects of how humans form and combine concepts are notoriously difficult to capture formally. In this paper, we focus on the representation of three particular such aspects, namely overexten- sion, underextension, and dominance. Inspired in part by the work of Hampton, we consider concepts as given through a prototype view, and by considering the interdependencies between the attributes that define a concept. To approach this formally, we employ a recently introduced family of operators that enrich Description Logic languages. These operators aim to characterise complex concepts by collecting those instances that apply, in a finely controlled way, to âenoughâ of the conceptâs defin- ing attributes. Here, the meaning of âenoughâ is technically realised by accumulating weights of satisfied attributes and comparing with a given threshold that needs to be met
The interplay between models and observations
We propose a formal framework to examine the relationship between models and observations. To make our analysis precise, models are reduced to first-order theories that represent both terminological knowledge-e.g., the laws that are supposed to regulate the domain under analysis and that allow for explanations, predictions, and simulations-and assertional knowledge-e.g., information about specific entities in the domain of interest. Observations are introduced into the domain of quantification of a distinct first-order theory that describes their nature and their organization and takes track of the way they are experimentally acquired or intentionally elaborated. A model mainly represents the theoretical knowledge or hypotheses on a domain, while the theory of observations mainly represents the empirical knowledge and the given experimental practices. We propose a precise identity criterion for observations and we explore different links between models and observations by assuming a degree of independence between them. By exploiting some techniques developed in the field of social choice theory and judgment aggregation, we sketch some strategies to solve inconsistencies between a given set of observations and the assumed theoretical hypotheses. The solutions of these inconsistencies can impact both the observations-e.g., the theoretical knowledge and the analysis of the way observations are collected or produced may highlight some unreliable sources-and the models-e.g., empirical evidences may invalidate some theoretical law