Thursday, May 30, 2019
Alexandru Dragomir (University of Bucharest)
Protocols in Dynamic Epistemic Logic
Abstract:
Dynamic epistemic logics are useful in reasoning about knowledge and certain acts of learning
(epistemic actions). However, not all epistemic actions are allowed to be executed in an initial
epistemic model, and this is where the concept of a protocol comes in: a protocol stipulates what
epistemic actions are allowed to be performed in a model. The aim of my presentation is to introduce
the audience to two accounts of protocols in DEL: one based on [1], and the second on [2].
References:
[1] T. Hoshi, Epistemic dynamics and protocol information, PhD thesis, Stanford University, 2009.
[2] Y. Wang, Y. Epistemic Modelling and Protocol Dynamics, PhD thesis, University of Amsterdam, 2010.
Thursday, May 16, 2019
Ionuţ Ţuţu (Royal Holloway University of London & IMAR)
An introduction to hybrid-dynamic first-order logic
Abstract:
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about
reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic
with features that are common to hybrid and to dynamic logics. This provides certain key advantages
for dealing with reconfiguration, such as: (a) a signature of nominals, including operation and relation
symbols, that allows references to specific possible worlds / system configurations – as in the case of
hybrid logics; (b) distinguished signatures of rigid and flexible symbols, where the rigid symbols are
interpreted uniformly across possible worlds – this supports a rigid form of quantification, which ensures
that variables have the same interpretation regardless of the possible world where they are evaluated;
(c) hybrid terms, which increase the expressive power of the logic in the context of rigid symbols; and (d)
modal operators over dynamic-logic actions, which are defined as regular expressions over binary nominal relations.
In this context, we advance a notion of hybrid-dynamic Horn clause and develop a series of results
that lead to an initial-semantics theorem for the Horn-clause fragment of hybrid-dynamic first-order logic.
Thursday, April 10, 2019
Mihai Prunescu (University of Bucharest)
Around Hilbert's Tenth Problem
Abstract: We discuss different implications of the negative answer of Hilbert's Tenth Problem:
the exponential diophantine equation over ${\mathbb N}$ and ${\mathbb Q}$, the minimal number of
variables which lead to an undecidable problem over ${\mathbb Z}$, the homogenous diophantine problem over ${\mathbb Z}$.
Thursday, March 28, 2019
Mihai Prunescu (University of Bucharest)
Lindström's Theorems II
Thursday, March 14, 2019
Mihai Prunescu (University of Bucharest)
Lindström's Theorems
Abstract: Regular logic systems which are strictly stronger than the first order
predicate calculus cannot satisfy in the same time Löwenheim-Skolem for statements and compacity (Lindström 1).
Effectively presented such systems cannot satisfy in the same time Löwenheim-Skolem for statements and
the condition that the set of generally valid sentences is recursively enumerable (Lindström 2).
We sketch the proof that uses partial isomorphisms.
References:
[1] H.-D. Ebbinghaus, J. Flum, W. Thomas, Mathematical Logic. Second edition, Undergraduate Texts in Mathematics, Springer, 1996.
Thursday, February 28, 2019
Natalia Moangă (University of Bucharest)
The hybridization of many-sorted polyadic modal logic
Abstract: Hybrid logics are obtained by enriching modal logics with nominals and state variables, that
directly refer the individual points in a Kripke model.
In the present work we develop a hybrid version on top of our many-sorted polyadic logic, previously defined.
Our system has nominals and state variables on each sort, as well as binders that act like the universal and the existential
quantfiers on state variables. In doing this, we follow various approaches for hybrid modal logic, especially the work of
Blackburn and Tsakova.
Alexandru Dragomir (University of Bucharest)
An introduction to BAN logic (a logic of authentication)
Abstract: One of the first and most discussed logical approaches to the problem of
verifying security protocols is the one proposed in BAN logic (Burrows, Abadi & Needham 1989),
a many-sorted modal logic used for its intuitive and compelling set of inference rules devised
for reasoning about an agent’s beliefs, trust and message exchange. My presentation will focus on
(1) presenting the language and inference rules of BAN logic,
(2) following the original paper's analysis of the Otway-Rees protocol,
(3) presenting some objections to using BAN, and
(4) discussing the problem of offering a semantics of BAN logic.
Thursday, January 31, 2019 at 10:00 in Hall 214
Cătălin Dima (Université Paris-Est Créteil)
The frontier between decidability and undecidability for logics for strategic reasoning in the presence of imperfect information
Abstract: The last 15-20 years have seen a number of logical formalisms that focus on strategic reasoning.
These logics aim at giving specification languages for various multi-agent game structures,
in which agents have adversarial or cooperative objectives which may be qualitative or
quantitative and may have various types of imperfect information. The presence of imperfect
information raises a particular difficulty in that many games cannot be solved algorithmically,
as well as their corresponding logical formalisms. In this tutorial I will review some techniques
for proving that the Alternating-time Temporal Logic has an undecidable model-checking problem,
but this problem becomes decidable when considering memoryless strategies, coalitions with
distributed knowledge, hierarchical knowledge and public or coalition-public announcements.
I will also give a short introduction to the model-checking tool MCMAS which relies on
the memoryless semantics for ATL with imperfect information, and the problems that arise when
implementing the model-checking algorithms for this case.
Thursday, December 20, 2018
Andrei Sipoș (TU Darmstadt & IMAR)
The finitary content of sunny nonexpansive retractions
Abstract: The goal of proof mining is to extract quantitative information out of proofs
in mainstream mathematics which are not necessarily fully constructive. Often, such proofs make
use of strong mathematical principles, but a preliminary analysis may show that they are
not actually needed, so the proof may be carried out in a system of strength corresponding
roughly to first-order arithmetic. Following a number of significant advances in this vein
by Kohlenbach in 2011 and by Kohlenbach and Leuștean in 2012, we now tackle a long-standing
open question: the quantitative analysis of the strong convergence of resolvents in classes
of Banach spaces more general than Hilbert spaces.
This result was proven for the class of uniformly smooth Banach spaces by Reich in 1980.
What we do is to analyze a proof given in 1990 by Morales, showing that adding the hypothesis
of the space being uniformly convex, and thus still covering the case of $L^p$ spaces, can serve
to eliminate the strongest principles used in the proof by way of a modulus of convexity for
the squared norm of such spaces. A further procedure of arithmetization brings the proof down
to System $T$ so the proper analysis may proceed. After obtaining a non-effective realizer of
the metastability statement, this is majorized in order to obtain the desired rate.
Subsequent considerations calibrate this bound to $T_1$. It particular, this result completes
some analyses that had previously been obtained only partially, yielding rates of metastability
within the above-considered class of Banach spaces for the Halpern and Bruck iterations.
These results are joint work with Ulrich Kohlenbach.
References:
[1] U. Kohlenbach, A. Sipoș, The finitary content of sunny nonexpansive retractions,
arXiv:1812.04940 [math.FA], 2018.
Thursday, December 6, 2018
Roberto Giuntini (University of Cagliari)
Classical and quantum degrees of truth: a new look at the effects of a Hilbert space
Abstract: We investigate certain Brouwer-Zadeh lattices that serve as abstract counterparts
of lattices of effects in Hilbert spaces under the spectral ordering. These algebras, called
$PBZ^*$-lattices, can also be seen as generalisations of orthomodular lattices and are remarkable
for the collapse of three notions of “sharpness” that are distinct in general Brouwer-Zadeh lattices.
We investigate the structure theory of $PBZ^*$-lattices and their reducts; in particular, we prove
some embedding results for $PBZ^*$-lattices and provide an initial description of the lattice
of $PBZ^*$-varieties.