Dynamics in Logic III 

Date: 8 June 2015 Topics and aims: Dynamics
in
Logic will keep its goal of
bringing together a small group of people who are currently very active
in the area of logic and information dynamics. This edition will be
focused on proof theory and on the socalled "common sense reasoning"
(i.e. the actual reasoning of humans) as studied in artificial
intelligence.
Registration: none. Colocated event: Conference Teaching Tools for Logic (TTL 2015), 9  12 June, Rennes, France. Program:
Title: Uncertainty theories and nonmonotonic reasoning
Abstract:
Nonmonotonic reasoning clusters a number of logicrelated formalisms
that only share the fact of lacking the monotonicity property of
classical logic. This very unspecific feature covers a number of almost
unrelated calculi having various motivations, one of which being
exceptiontolerant reasoning. Knowledge representation and reasoning
systems to this end have been pioneered by Dov Gabbay and Yoav
Shoham, then extensively developed by Daniel Lehmann, Judea Pearl
and their colleagues from the mid 1980 till the mid 95. There exists
natural connections between these formalisms and theories of
uncertainty like probability theory and possibility theory. The
keyconnection between uncertainty theories and exceptiontolerant
nonmonotonic inference is the notion of conditioning, central to
uncertain reasoning, and absent from classical logic. The aim of the
talk is to show that conditional probability, once stripped from its
numerical clothes, exactly corresponds to a nonmonotonic conditional
assertion captured by preferential inference of Lehmann and colleagues
(without resorting to infinitesimals). Adding rational monotony leads
to a form of conditional modelled by conditional possibility and an
inference relation captured by possibilistic logic. This approach also
accounts for a notion of accepted defeasible beliefs that is
closed under logical consequences, and closely related to theory
revision, contrary to the usual notion of probabilistic
acceptance (studied especially by the late Henry Kyburg). Connections
with imprecise probability and modal logics of belief can thus be laid
bare as well. These results support the idea that the symbolic approach
to exception tolerant reasoning stands as a backbone to probabilistic
reasoning. The latter still obeys its basic principles (like
cumulativity), but in a degenerated (numerical) form. In this sense
this talk is a plea for a unified view of symbolic and numerical
approaches toexceptiontolerant reasoning.
Title: ProofTheory for conditional logics
Abstract:
Conditional logics have been proposed by Lewis, Stalnaker, Nute,
Chellas and Burgess, among others, to formalise a kind of hypothetical
implication that cannot be adequatly represented by material
implication of classical logic. Conditional logic have been used to
model several kinds of reasoning in Articifial Intelligence and
Epistemology (representing counterfactuals, reasoning about belief
change, prototypical properties and rules with exceptions). The proof
theory of conditional logics is not as developed as the one of other
extensions of classical logics, first of all modal logics of which they
are a sort of generalisation. It is particularly difficult to obtain
analytic and internal proof system for them. In the quest of calculi of
this kind, I shall present recently introduced nested sequent calculi
which seem particularly natural for conditional logics, at least for
the basic systems. Finally I shall discuss some open problems, in
particular the challenge of obtaining natural internal calculifor
strong conditional logics, such as Lewis’ logics of counterfactuals.
Title: A poor man's epistemic logic
Abstract:
We introduce a dynamic epistemic logic that is based on what an agent
can observe, including joint observation and observation of what other
agents observe. This generalizes previous approaches due to van der
Hoek, Wooldridge and others where it is common knowledge which
propositional variables each agent observes. Our approach is couched in
a dynamic logic where both facts of the world and their observability
can be modified by assignment programs. We show that in that dynamic
logic, epistemic operators reduce to particular programs. We also
provide a sound and complete axiomatization and prove that the
satisfiability problem is PSPACEcomplete. Finally, we show how public
and private announcements can be expressed. (joint work with Emiliano
Lorini and Faustine Maffre)
Title: Introspection, Normality, Agglomeration
Abstract:
This talk reports on joint work with Olivier Roy and Norbert Gratzl. We
explore a nonnormal logic of beliefs for boundedly rational agents.
The logic we study is the result of dropping positive introspection for
knowledge in the system developed by Stalnaker . In that system beliefs
are not closed under conjunction, but they are required to be pairwise
consistent, a requirement that has been called agglomerativity
elsewhere. While bounded agglomerativity requirements, i.e., joint
consistency for every ntuple of beliefs up to a fixed n, are
expressible in that logic, unbounded agglomerativity is not. We
study an extension of this logic of beliefs with such an unbounded
agglomerativity operator. We provide sound and complete axiomatizations
for both logics, show that they have the finite model property and
explore dynamical properties.
Title and abstract: Displaying dynamic logics and beyond
Title: Dynamic Epistemic Logic in Update Logic
Abstract:
We generalize the language of substructural logics interpreted over the
ternary relational semantics. We introduce three symetric triples of
connectives which are interconnected by means of cyclic permutations.
The usual fusion, implication and coimplication connectives form one
of these triples. This defines a logic that we call update logic. We
define a cutfree display calculus for update logic which generalizes
the display calculus for modal logic and a sequent calculus for update
logic which generalizes the nonassociative Lambek calculus. Then, we
provide a display calculus as well as a sequent calculus for dynamic
epistemic logic based on our display and sequent calculifor update logic.
Title: Epistemic Logics for Sceptical Agents
Abstract:
We present a framework based on a knowledge modality defined as a
diamond operator over distributive nonassociative full Lambek calculus
with a negation. We deal with the relational semantics for distributive
substructural logics, interpreting the elements of a relational frame
as information states consisting of collections of data which may be
incomplete or even inconsistent. We explicate the notion of knowledge
as information confirmed by a reliable source. The system is modular in
the sense that the axiomatization of the epistemic operator is sound
and complete with respect to various background propositional logics,
which makes the system potentially applicable to a wide class of
epistemic contexts. Our system admits a weak form of logical
omniscience (the monotonicity rule), but avoids stronger ones (the
necessitation rule and the Kaxiom) as well as some closure properties
discussed in normal epistemic logics (like the positive and negative
introspection). For these properties we provided characteristic frame
conditions, so that they can be present in the system if they are
considered to be appropriate for some specific epistemic context.
Local organizer: Guillaume Aucher Previous editions: 




Last update: 29 May 2015 