Dear all,
We will have our next LIRa session on Thursday, April 8th. Our speaker is Marta Bilkova. You can find the details of the talk below. We will use our recurring zoom link: https://uva-live.zoom.us/j/92907704256?pwd=anY3WkFmQVhLZGhjT2JXMlhjQVl1dz09 (Meeting ID: 929 0770 4256, Passcode: 036024).
Speaker: Marta Bilkova
Date and Time: Thursday, April 8th 2021, 16:30-18:00, Amsterdam
time.
Venue: online.
Title: Belief based on inconsistent information.
Abstract. When it comes to information, its potential incompleteness,
uncertainty, and contradictoriness needs to be dealt with adequately.
Separately, these characteristics have been taken into account by
various appropriate logical formalisms and (classical) probability
theory. While incompleteness and uncertainty are typically
accommodated within one formalism, e.g. within various models of
imprecise probability, contradictoriness and uncertainty less so ---
conflict or contradictoriness of information is rather chosen to be
resolved than to be reasoned with. To reason with conflicting
information, positive and negative support---evidence in favour and
evidence against---a statement are quantified separately in the
semantics. This two-dimensionality gives rise to logics interpreted
over twisted-product algebras or bi-lattices, e.g. the well known
Belnap-Dunn logic of First Degree Entailment.
In this talk, we introduce many-valued paraconsistent logics for
uncertainty which are interpreted over twisted-product algebras based
on the [0,1] real interval. They can be seen to account for the
two-dimensionality of positive and negative component of (the degree
of) belief based on potentially contradictory information. The logics
include extensions of Łukasiewicz or Gödel logic with a de-Morgan
negation which swaps between the positive and negative component. The
extensions of Gödel logic in particular turn out to be extensions of
Nelson\'s paraconsistent logic N4, or Wansing\'s paraconsistent logic
I_4C_4, with the prelinearity axiom. The logics inherit completeness
and decidability properties of Łukasiewicz or Gödel logic
respectively.
They can be applied to reason about belief based on evidence: In [1],
a logical framework in which belief is based on potentially
contradictory information obtained from multiple, possibly
conflicting, sources and is of a probabilistic nature, has been
suggested, using a two-layer modal logical framework to account for
evidence and belief separately. The logics above are the logics used
on the upper level in this framework. The lower level uses Belnap-Dunn
logic to model evidence, and its probabilistic extension to give rise
to a belief modality.
(Based on joint work with S. Frittella, D. Kozhemiachenko, O. Majer,
and S. Nazari.)
[1] M. Bílková, S. Frittella, O. Majer and S. Nazari: Belief based
on inconsistent information, DaLi 2020: Dynamic Logic. New Trends and
Applications (M.A. Martins and I. Sedlar, editors), LNCS, vol. 12569,
Springer, 2020, pp. 68–86.
Hope to see you there!
The LIRa team
