Thursday, June 9, 2016
Denisa Diaconescu (University of Bucharest)
Skolemization for Substructural Logics
Abstract: The usual Skolemization procedure, which removes strong quantifiers by
introducing new function symbols, is in general not sound for first-order substructural logics.
However, in this talk, we will show that first-order substructural logics with a semantics
satisfying certain witnessing conditions admit a "parallel" Skolemization procedure where
a strong quantifier is removed by introducing a finite disjunction or conjunction (as appropriate)
of formulas with multiple new function symbols.
Thursday, June 2, 2016
Daniela Cheptea (University of Bucharest)
Reticulation of hoops
Abstract: Hoops are ordered structures introduced by B. Bosbach under the name of complemented semigroups.
We present the reticulation of a hoop, which is a bounded distributive lattice with the property that
there exists a homeomorphism between its prime spectrum and the prime spectrum of the hoop.
We give an axiomatic definition of the reticulation and we prove that the reticulation is unique
modulo a lattice isomorphism. Furthermore, we define a covariant functor between the category
of bounded distributive lattices and the category of bounded hoops, which allows us to obtain
new properties from the properties of lattices.
Thursday, May 19, 2016
Andrei Sipoș (IMAR & University of Bucharest)
Proof mining and families of mappings
Abstract: We present the general metatheorems of proof mining for Hilbert spaces and
a concrete case on how they might be applied - specifically, the convergence theorem of
Lopez-Acedo and Xu for a finite families of pseudo-contractive self-mappings of a convex set
in a Hilbert space, for which we shall compute a rate of asymptotic regularity.
Thursday, April 14, 2016
Traian Şerbănuţă (University of Bucharest)
Ioana Leuştean (University of Bucharest)
Mircea Dumitru (University of Bucharest)
Mihai Prunescu (IMAR)
Mircea Dumitru (University of Bucharest)
Mihai Prunescu (IMAR)
Mihai Prunescu (IMAR)
Laura Franzoi (University of Bucharest and University of Trieste)
Andrei Sipoș (IMAR & University of Bucharest)
Andrei Sipoș (IMAR & University of Bucharest)
Andrei Sipoș (IMAR & University of Bucharest)
Andrei Sipoș (IMAR & University of Bucharest)
Andrei Sipoș (IMAR & University of Bucharest)
Traian Şerbănuţă (University of Bucharest)
12:00
11:100
Traian Şerbănuţă (University of Bucharest)
Traian Şerbănuţă (University of Bucharest)
10:00
11:15
Traian Şerbănuţă (University of Bucharest)
Traian Şerbănuţă (University of Bucharest)
Traian Şerbănuţă (University of Bucharest)
Traian Şerbănuţă (University of Bucharest)
Mihai Prunescu (IMAR)
Mihai Prunescu (IMAR)
Partial membership equational logic
Abstract:
This talk will review (Partial) Membership Equational Logic as introduced by Meseguer [2]
and will present some development and results about a class of algebraic specifications
(presentations) which admit the same set of consequences regardless whether they are interpreted
in the total or in the partial membership equational logic [1].
References:
[1] J. Meseguer, G. Roşu,
A Total Approach to Partial Algebraic Specification, ICALP 2002: 572-584
LNCS.
[2] J. Meseguer, Membership algebra as
a logical framework for equational specification, WADT 1997: 18-61.
Thursday, April 7, 2016
Finitely presented structures in Łukasiewicz logic
Abstract:
In this talk we will present Łukasiewicz logic and its extension obtained by adding a scalar
multiplication. We will analyze the connections between logic, algebra and the theory of polyhedra,
with a special emphasis on finitely presented structures.
Thursday, March 31, 2016
Abstract Free Logic for Fictionalism II
Thursday, March 24, 2016
A many-sorted approach to the Special Theory of Relativity III
Thursday, March 17, 2016
Abstract Free Logic for Fictionalism
Abstract:
Fictionalism is a fashionable and timely doctrine in many quarters of contemporary philosophy.
It has fueled and channeled important debates in metaphysics (ontology), philosophy of language and
philosophical logic, for its having a genuine explanatory virtue: even if it is extremely hard to buy
into the full ontological existence of, say, unobservable things, or abstract things, or fictional objects,
or nonfactual (and merely possible) things, or even moral values, one could, nevertheless, endorse forms
of meaningful discourse which are about those sui-generis objects. Various kinds of fictionalism will
help us in this regard: the things on which we think in those forms of discourse have to
be accepted by us, even if they do not qualify ontologically, semantically, or epistemologically
as being truth-apt or as truth-makers or truth-bearers. Against this background, my paper
aims at disentangling certain logical principles that govern the meaningful fictional
discourse on fictional objects. The ontological thesis concerning fictional objects that
I endorse is that fictional objects are essentially objects of reference, i.e. objects
created through a story or a narrative and introduced via a cluster of descriptions. The main
point that I am going to make in my paper is this: in order to articulate the logical principles
which govern the meaningful discourse on fictional objects what we need is a sort of free logic.
The issue is: what kind? Now, a major motivation for developing free logics systems has
always been to provide a basis for theories of definite descriptions. Having in view the
essential connection between any given fictional object term and the cluster of descriptions
through which the former is introduced, I argue that the kind of logic we need for fictionalism
and fictional objects discourse is a positive free logic with free descriptions.
Thursday, March 10, 2016
A many-sorted approach to the Special Theory of Relativity II
Thursday, March 2, 2016
A many-sorted approach to the Special Theory of Relativity
Abstract:
We deduce the Lorentz and the Galilean transformation rules in a many-sorted first-order
structure where moving points and moving frames are abstract sorts. If we suppose that the
set of speeds allowed for the relative movement of frames is an interval, then both transformation
rules can be proven if one states orientation, compatibility with the relative speed, symmetry,
and an axiom about the existence or non-existence of an invariant speed. The case generally
known as Spherical Relativity (a < 0) is inconsistent with the supposition that the set of speeds
is an interval. If we allow more general convex sets as sets of speeds, there are models of the
Spherical Relativity as well. In this case the class of ground fields is exactly the class
of non-archimedean Euclidean ordered fields.
Thursday, February 25, 2016
Distribution calculus: maxitive probabilities vs. additive probabilities
Abstract:
Some incongruences met in fuzzy arithmetic are dispelled when one uses systematically maxitive possibilities,
and so multi-valued logic, rather than fuzzy sets, and imports time-honoured notions used in random
arithmetic, i.e. in distribution calculus for random variables, priviliging Pitt's "implicit" definition
of random variables w.r. to Kolmogorov's "explicit" definition, equivalent but not so convenient
to be exported into a maxitive theory. In particular, we focus on the notion of irrelevance, due to the
talker jointly with A. Sgarro, which remarkably expedites computations w.r. to a more standard
approach to fuzzy arithmetic.
Thursday, February 18, 2016, Hall 220
Applied Proof Theory V
Thursday, February 11, 2016, Hall 220
Applied Proof Theory IV
Thursday, February 4, 2016, Hall 220
Applied Proof Theory III
Thursday, January 28, 2016, Hall 220
Applied Proof Theory II
Thursday, January 21, 2016, Hall 220
Applied Proof Theory I
Abstract:
We aim to provide a comprehensive introduction to proof mining, an area of applied logic that
has as its goal the extraction of "quantitative information" (i.e. realizers and bounds)
from proofs of an apparently non-constructive nature. We begin with a description of the
specific logical systems that are usually worked with in this endeavour.
Thursday, January 14, 2016, Hall 220
Matching Logic VII
Thursday, January 7, 2016, 12:00-14:00, Hall Spiru Haret
Claudia Chiriță (Royal Holloway University of London)
Free Jazz and Service-Oriented Improvisations
Abstract:
Building on a concept of many-valued institution (called RL-institution) in which the truth
spaces are residuated lattices, we study free jazz improvisations in the context of
Service-Oriented Computing. We define an RL-institution of graphical notations for Free
Jazz, and describe how it can be used to capture music fragments as specifications over this
logic. We then model musical improvisations by means of processes of service-oriented discovery, selection and binding.
Ionuț Țuțu (Royal Holloway University of London)
Multiple-parameterized behavioural specifications
Abstract:
Behavioural specification, based on Horst Reichel's notion of behavioural satisfaction, is
nowadays one of the most promising algebraic specification paradigms. In this talk, we review
a recently proposed axiomatic framework of structured behavioural specifications and put
forward a dedicated theory of pushout-style parameterization that supports generic behavioural s
pecifications with multiple parameters and implicit sharing. We explain when - and also how - it
is possible to simultaneously or sequentially instantiate multiple-parameterized behavioural
specifications, and discuss some of the additional conditions that need to be imposed in order
to guarantee that the results of the two instantiation procedures are isomorphic.
Thursday, December 10, 2015, Hall 220
Matching Logic VI
Thursday, December 3, 2015, Hall 220
Matching Logic V
Thursday, November 26, 2015, Hall 220
Jacek Malinowski (Polish Academy of Sciences)
Theory of Logical Consequence - past, present and future
Abstract:
The aim of the lecture is to give a general review of old and more recent results, as well as,
possible future developments in the theory of logical consequence operation.
Serafina Lapenta (University of Salerno)
Convex MV-algebras
(joint work with Tommaso Flaminio)
Abstract:
The notions of convexity plays a central rôle in logic and mathematics.
Starting from a seminal idea of Brown [1], we propose an axiomatic approach to convex
combinations in the realm of MV-algebras [2].
More in detail, we will expand the language of MV-algebras by an uncountable family of binary
operations $cc_\alpha(\cdot, \cdot)$ (one for every $\alpha\in [0,1]$) axiomatized so to
capture the basic properties of convex combinations in $[0,1]$. The so resulting algebras are
called convex MV-algebras (or CMV-algebras for short).
CMV-algebras form a variety. Our first result shows that CMV-algebras are termwise equivalent
to Riesz MV-algebras [3] and, consequently, the variety of CMV-algebras is generated
by the standard CMV-algebra, that is the standard MV-algebra where the operators
$cc_\alpha$ are interpreted in the usual way: for each $x,y,\alpha\in [0,1]$,
$cc_\alpha(x,y)$ is $\alpha x+(1-\alpha)y$.
States of MV-algebras [4] are analogous to finitely additive probabilities
on boolean algebras and, for every MV-algebra ${\bf A}$, its states form a subset of
$[0,1]^A$ which coincide with the topological closure of the convex hull of the MV-homomorphisms
of ${\bf A}$ in the standard MV-algebra $[0,1]_{MV}$. Thanks to this characterization of
the states space, we will show that each state of a finitely dimensional MV-algebra
$[0,1]^X$ (with $X$ finite) has a faithful representation in the free CMV-algebra $|X|$-generated.
References:
[1] N. P. Brown, Topological Dynamical Systems Associated to $\Pi_1$-factors, preprint arXiv:1010.1214.
[2] R. Cignoli, I. M. L. D'Ottaviano, D. Mundici, Algebraic Foundations of Many-valued Reasoning,
Trends in Logic Vol 8, Kluwer, Dordrecht, 2000.
[3] A. Di Nola, I. Leuștean, Łukasiewicz logic and Riesz Spaces, Soft Computing,
Soft Comp. 18(12) (2014) 2349-2363. arXiv:1309.1575v1
[4] D. Mundici, Averaging the Truth-value in Łukasiewicz Logic. Studia Logica 55(1), 113--127, 1995.
Thursday, November 19, 2015, Hall 220
Matching Logic IV
Thursday, November 12, 2015, Hall 220
Matching Logic III
Thursday, November 5, 2015, Hall 220
Matching Logic II
Thursday, October 29, 2015, Hall 220
Matching Logic
Abstract:
Matching Logic, recently introduced by Grigore Roşu, is a logic for specifying and reasoning
about structure by means of patterns and pattern matching. Its syntax is an extension of
the FOL syntax; however, its semantics is interpreted over multi-algebras instead of standard
first order models. The talk will introduce Matching Logic by means of examples, present
known results about the logic, and discuss its relation to FOL and Reynolds' Separation Logic.
Thursday, October 22, 2015, Hall 220
Continuous p-adic functions II
Thursday, October 15, 2015, Hall 220
Continuous p-adic functions
Abstract: In the reference book "$p$-adic numbers and their functions" (1973) Kurt Mahler described the continuous functions $f: \mathbb{Z}_p \rightarrow \mathbb{Q}_p$. He proved that $f$ is continuous according to the $p$-adic topology if and only if it has a series expansion $f(x) = \sum\limits_{n=0}^\infty a_n \binom{x}{n}$, where $a_n \rightarrow 0$ according to the same topology.