77 research outputs found
Logics for modelling collective attitudes
We introduce a number of logics to reason about collective propositional
attitudes that are defined by means of the majority rule. It is well known that majoritarian
aggregation is subject to irrationality, as the results in social choice theory and judgment
aggregation show. The proposed logics for modelling collective attitudes are based on
a substructural propositional logic that allows for circumventing inconsistent outcomes.
Individual and collective propositional attitudes, such as beliefs, desires, obligations, are
then modelled by means of minimal modalities to ensure a number of basic principles. In
this way, a viable consistent modelling of collective attitudes is obtained
A Logic for Reasoning about Group Norms
We present a number of modal logics to reason about group norms. As a preliminary
step, we discuss the ontological status of the group to which the norms are
applied, by adapting the classification made by Christian List of collective attitudes
into aggregated, common, and corporate attitudes. Accordingly, we shall introduce
modality to capture aggregated, common, and corporate group norms. We investigate
then the principles for reasoning about those types of modalities. Finally, we discuss
the relationship between group norms and types of collective responsibility
Non-normal modalities in variants of Linear Logic
This article presents modal versions of resource-conscious logics. We
concentrate on extensions of variants of Linear Logic with one minimal
non-normal modality. In earlier work, where we investigated agency in
multi-agent systems, we have shown that the results scale up to logics with
multiple non-minimal modalities. Here, we start with the language of
propositional intuitionistic Linear Logic without the additive disjunction, to
which we add a modality. We provide an interpretation of this language on a
class of Kripke resource models extended with a neighbourhood function: modal
Kripke resource models. We propose a Hilbert-style axiomatization and a
Gentzen-style sequent calculus. We show that the proof theories are sound and
complete with respect to the class of modal Kripke resource models. We show
that the sequent calculus admits cut elimination and that proof-search is in
PSPACE. We then show how to extend the results when non-commutative connectives
are added to the language. Finally, we put the logical framework to use by
instantiating it as logics of agency. In particular, we propose a logic to
reason about the resource-sensitive use of artefacts and illustrate it with a
variety of examples
Ontology Merging as Social Choice
The problem of merging several ontologies has important applications in the Semantic Web, medical ontology engineering
and other domains where information from several distinct sources needs to be integrated in a coherent manner.We propose
to view ontology merging as a problem of social choice, i.e. as a problem of aggregating the input of a set of individuals
into an adequate collective decision. That is, we propose to view ontology merging as ontology aggregation. As a first step in
this direction, we formulate several desirable properties for ontology aggregators, we identify the incompatibility of some of
these properties, and we define and analyse several simple aggregation procedures. Our approach is closely related to work
in judgment aggregation, but with the crucial difference that we adopt an open world assumption, by distinguishing between
facts not included in an agent’s ontology and facts explicitly negated in an agent’s ontology
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 cognitive view of relevant implication
Relevant logics provide an alternative to classical implication
that is capable of accounting for the relationship between the antecedent
and the consequence of a valid implication. Relevant implication is usually
explained in terms of information required to assess a proposition.
By doing so, relevant implication introduces a number of cognitively relevant
aspects in the denition of logical operators. In this paper, we
aim to take a closer look at the cognitive feature of relevant implication.
For this purpose, we develop a cognitively-oriented interpretation of the
semantics of relevant logics. In particular, we provide an interpretation
of Routley-Meyer semantics in terms of conceptual spaces and we show
that it meets the constraints of the algebraic semantics of relevant logic
Modelling Multilateral Negotiation in Linear Logic
We show how to embed a framework for multilateral negotiation,
in which a group of agents implement a sequence of deals
concerning the exchange of a number of resources, into linear logic.
In this model, multisets of goods, allocations of resources, preferences
of agents, and deals are all modelled as formulas of linear logic.
Whether or not a proposed deal is rational, given the preferences of
the agents concerned, reduces to a question of provability, as does
the question of whether there exists a sequence of deals leading to an
allocation with certain desirable properties, such as maximising social
welfare. Thus, linear logic provides a formal basis for modelling
convergence properties in distributed resource allocation
Modelling Combinatorial Auctions in Linear Logic
We show that linear logic can serve as an expressive framework
in which to model a rich variety of combinatorial auction
mechanisms. Due to its resource-sensitive nature, linear
logic can easily represent bids in combinatorial auctions in
which goods may be sold in multiple units, and we show
how it naturally generalises several bidding languages familiar
from the literature. Moreover, the winner determination
problem, i.e., the problem of computing an allocation of
goods to bidders producing a certain amount of revenue for
the auctioneer, can be modelled as the problem of finding a
proof for a particular linear logic sequent
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
Gärdenfors'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
Repairing Ontologies via Axiom Weakening.
Ontology engineering is a hard and error-prone task, in which
small changes may lead to errors, or even produce an inconsistent
ontology. As ontologies grow in size, the need for automated
methods for repairing inconsistencies while preserving
as much of the original knowledge as possible increases.
Most previous approaches to this task are based on removing
a few axioms from the ontology to regain consistency.
We propose a new method based on weakening these axioms
to make them less restrictive, employing the use of refinement
operators. We introduce the theoretical framework for
weakening DL ontologies, propose algorithms to repair ontologies
based on the framework, and provide an analysis of
the computational complexity. Through an empirical analysis
made over real-life ontologies, we show that our approach
preserves significantly more of the original knowledge of the
ontology than removing axioms
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