Special Session on Substructural logics, information and interaction

Monday 24 January we will have the first special session of the seminar in 2011. The general topic of discussion will be Substructural logics, information and interaction.

The session will start at 14:00 hrs, and will take place inĀ  C0.23 of OMHP (a map pf the location can be found here). The special session will have the following program:

14:00 – 14:40 Daniele Porello
Modeling Resource Allocation in Linear Logic

In the last decades, resource allocations problems have been widely investigated also from a computational point of view both in the AI and the logic community. In this presentation, I will show how substructural logics, and linear logic in particular, provide a principled modeling of resources allocation problems, which can be classified according to the types of goods agents trade. I will present a classification of resource allocation problems with the corresponding logical language to encode preferences and we will see how dropping contraction, weakening or exchange affects the type of goods on which agents express their valuations.
It is interesting to stress that, in this framework, the process of allocating goods to agents can be modeled by the notion of proof in some suitable fragments of linear logic.
This presentation is based on two joint works with Ulle Endriss (KR 2010 and ECAI 2010).

14:40 – 14:50 Questions and Discussion
14:50 – 14:00 Coffee Break

15:00 – 15:40 Sebastian Sequoiah-Grayson
Modeling Epistemic Actions

Epistemic actions such as acts of deductive reasoning, communication,
and observation, saturate our rational lives. Such actions play the
epistemically crucial roles that they do due to the fact that we lack
certain fantastic epistemic abilities – logical omniscience,
clairvoyance, and omniscience respectively. We will see how it is that
that the limits of such actions correspond to various subsystem
thresholds of the database corresponding to the total universe of
information. The dynamic properties of the actions that facilitate
such convergence are modeled by various substructural logics. In
detail, we will see how it is that the dynamic properties of deductive
information processing are modeled by the operational semantic frames
corresponding to the categorical grammar marked by mobiles;
bracket-sensitive commuting structures.

Keywords: epistemic actions, information, omniscience, operational
semantics, categorical grammar.

15:40 – 15:50 Questions and Discussion
15:50 – 16:00 Coffee break

16:00 – 16:40 Michael Moortgat
Syntax and Semantics in Generalized Lambek Calculus
The syntactic calculus, as proposed by Lambek in 1961, is a logic
completely without structural rules: rules affecting multiplicity
(contraction, weakening) or structure (commutativity, associativity) of
the grammatical resources are not considered. Originally conceived with
linguistics in mind, Lambek’s calculus (both the ’61 and the
associative ’58 variant or its modern pregroup incarnation) have
found many models outside linguistics: as the logic for composition of
informational actions, for example, and in fields such as mathematical
morphology or quantum physics.
In terms of expressivity, Lambek’s calculi are strictly context-free.
The context-free limitation makes itself felt in situations
where syntactic and semantic composition seem to be out of sync:
long distance dependencies in syntax, or the dynamics of scoping
in semantics. Competing frameworks in the ‘mildly context-sensitive’
family (TAG, MG, MCFG, etc) handle such phenomena gracefully.
In the talk, I discuss the Lambek-Grishin calculus, a symmetric
generalization of the syntactic calculus allowing multiple conclusions.
I focus on two features that help resolve tensions at the syntax-semantics
-A continuation-passing-style interpretation, making contexts an
explicit part of the composition process. As a result of the richer
view on the mapping between syntax and semantics, the syntactic
source calculus itself can be kept very simple.
-Distributivity principles relating Lambek’s original type-forming
operations and their duals. These principles characterize syntactic
deformations under which interpretations are stable. They allow
a quite natural treatment of patterns beyond CF.
Background reading
Moortgat 2009, Symmetric categorial grammar. J Philosophical Logic
38 (6):681-710.
16:40 – 16:50 Questions and Discussion
16:50 – 17:00 General Discussion