31 Jan 2018
Paris, France
Modal and Many-Valued Logics
Workshop
January 31, 2018
École Normale Supérieure
Salle Théodule Ribot
29, rue d'Ulm
75005 Paris
Workshop organized by École Normale Supérieure and Institut d?Histoire et
de Philosophie des Sciences et des Techniques, with funding from the
University Paris 1 Panthéon-Sorbonne and the project ?New Ideas in
Mathematical Philosophy? (DEC-ENS).
*Program*
9:00 ? 9:50 ? Andreas Herzig (CNRS, IRIT), A poor man?s epistemic logic
based on propositional assignment and higher-order observation (joint work
with Emiliano Lorini and Faustine Maffre)
9:50 ? 10:40 ? Paul Égré (CNRS, ENS), Varieties of logical consequence and
Suszko's Problem (joint work with Emmanuel Chemla)
10:40 ? 10:50 ? coffee break
10:50 ? 11:40 ? Allard Tamminga (University of Groningen, Utrecht
University), Two-sided sequent calculi for FDE-like four-valued logics
11:40 ? 12:30 ? Ekaterina Kubyshkina (Paris 1, IHPST), On modal
translation of many-valued logics
--
*Abstracts*
Andreas Herzig (joint work with Emiliano Lorini and Faustine Maffre)
A poor man?s epistemic logic based on propositional assignment and
higher-order observation
We introduce a dynamic epistemic logic that is based on what an agentcan
observe, including joint observation and observation of what other agents
observe. This generalizes van der Hoek,Wooldridge and colleague?s logics
ECLPC(PO) and LRC where it is common knowledge which propositional
variables each agent observes. In our logic, facts of the world and their
observability can both be modified by assignment programs. We show how
epistemic operatorscan be interpreted in this framework and identify the
conditions under whichthe principles of positive and negative
introspection are valid. Finally, we show how public and private
announcements can be expressed and illustrate the latter by the gossip
spreading problem.
--
Paul Égré (joint work with Emmanuel Chemla)
Varieties of logical consequence and Suszko's Problem
Suszko's problem is the problem of finding the minimal number of truth
values needed to semantically characterize a syntactic consequence
relation. Suszko proved that every Tarskian consequence relation can be
characterized using only two truth values. Malinowski showed that this
number can equal three if some of Tarski's structural constraints are
relaxed. By so doing, Malinowski introduced a case of so-called mixed
consequence (following Cobreros et al. 2012?s terminology), allowing the
notion of a designated value to vary between the premises and the
conclusions of an argument. In this paper we give a more systematic
perspective on Suszko's problem and on the characterization of mixed
consequence relations more generally. First, we prove general
representation theorems relating structural properties of a consequence
relation to their semantic counterparts. Based on those we derive and
strengthen maximum-rank results proved recently by French and Ripley
(2017), and by Blasio, Wansing and Marcos (2017) in a different setting
for logics with various structural properties (reflexivity, transitivity,
none, or both). We use those results to discuss the foundational problem
of what to admit as a bone fide consequence relation in logic.
--
Allard Tamminga
Two-sided sequent calculi for FDE-like four-valued logics
We present a general modular method to generate cut-free, two-sided
sequent calculi for four-valued logics like first degree entailment (FDE).
Our method relies on correspondences between truth-table entries and
sequent rules. First,we show that for every truth-functional n-ary
operator * every truth-table entry f*(x1, . . . ,xn) = y can be
characterized in terms of two sequent rules. Consequently, every
truth-functional n-ary operator can be characterized in terms of 2x4^n
sequent rules. Secondly, we build sequent calculi on the basis of these
characterizing sequent rules and prove completeness for every sequent
calculus with respect to its particular semantics. Lastly, we show that
the 2x4^n sequent rules that characterize an n-ary operator can be
systematically reduced to at most four sequent rules.
--
Ekaterina Kubyshkina
On modal translation of many-valued logics
Kooi and Tamminga (2013) define a Translation Manual that converts any
formula of any three-valued propositional logic into a modal formula. This
Translation Manual permits to show that every three-valued valuation has
an equivalent S5-model and vice versa. The authors remark that an
analogical result can be introduced for any four-valued propositional
logic and modal logic interpreted on minimal models M = <W, N, V>, where N
is a universal neighborhood. The universality of the neighborhood imposed
on the model, as well as the restriction to a S5-model in a three-valued
case, are strong and not always desirable conditions. In our talk we
modify the Translation Manual for the case of four-valued logics. This
shows that the universality of neighborhoods may be replaced by the
D-condition (also known as the consistency condition, it corresponds to
the D-axiom). The D-condition is weaker than the universality condition
and in some cases (especially if the modal operators are interpreted
epistemically) is more desirable. We exemplify our proposal on a specific
four-valued logic introduced by Kubyshkina and Zaitsev (2016). Our
technique may be also applied to the three-valued case and it provides a
way to avoid the restriction to S5-models.
--
*Organizers*
Paul Égré (paul.egre@ens.fr <mailto:paul.egre@ens.fr>)
Ekaterina Kubyshkina (ekaterina.kubyshkina@univ-paris1.fr
<mailto:ekaterina.kubyshkina@univ-paris1.fr>)
--
This event is taking place in the context of Ekaterina Kubyshkina's PhD
defense ("La logique de l'agent rationnel" / "The Logic of Rational
Agent"), Université Paris 1 Panthéon-Sorbonne, January 30, 2018,
http://www.ihpst.cnrs.fr/activites/autres/soutenance-de-these-ekaterina-kubyshkina
<http://www.ihpst.cnrs.fr/activites/autres/soutenance-de-these-ekaterina-kubyshkina>).
--
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