## 2nd Workshop on the Objects and Grounds of Structural Rules

**New Perspectives on the Objects and Grounds of Structural Rules 2**

TIME AND PLACE:

April 15^{th}–16^{th} 2024, 10:00–18:30

University of Lisbon

Faculty of Letters, Room B112.B

THEME:

Showing that a conclusion is a logical consequence of some premises typically requires two distinct kinds of rules. To wit, it requires operational rules, which codify the behaviour of the logical operations (negation, conjunction, universal quantification etc.). But it also requires structural rules, which govern instead the ways in which the premises and conclusions of an argument are structured, independently of the logical operations which appear in them (an example is the structural rule of commutativity, which states, roughly, that the order of the premises or conclusions does not matter). On the basis of this distinction, it is possible to characterise uniformly a multitude of non-classical logics that have in effect in common the feature of denying some structural rules of classical logic (but that may actually agree with classical logic concerning instead its basic operational rules). These logics are nowadays known as “substructural logics”: logics that are weaker than classical logic in that they deny at least one of its structural rules.

Substructural logics have had important philosophical applications in several areas (logical pluralism, rivalry between logics, paradoxes etc.). In these applications, structural rules are typically understood from the standpoint of what may well be called the “orthodox interpretation”, according to which they codify properties of the relation of logical consequence and such properties are fundamental with respect to the logical operations. The workshop will discuss this orthodox interpretation and, more generally, will examine the conceptual foundations of substructural logics and their philosophical applications.

SCHEDULE:

April 15th

10:00–11:30: Heinrich Wansing (Ruhr University Bochum), ‘From Bilateralism to Nontrivial Negation Inconsistency’

coffee break

12:00–13:30: Davood Hosseini (Tarbiat Modares University), ‘Sequent Calculus for First-Order Logic of Weak Formal Ground’ (online)

lunch

15:00–16:30: Elia Zardini (Complutense University of Madrid), ‘Totality=Every; Dependence=Some; Choice=Any; Chance=A Certain’

coffee break

17:00–18:30: Carlos Benito (University of Lisbon), ‘Substructural and Localist Approaches to Mixed Reasoning’

aperitif and dinner

April 16th

10:00–11:30: Pilar Terrés (University of Valencia), ‘Contextual Minimalism’

coffee break

12:00–13:30: Bogdan Dicher (University of the Witwatersrand), ‘Meaning and Substructural Rules’

lunch

15:00–16:30: Gilda Ferreira (Open University), ‘The Russell-Prawitz Translation: Alternative Approaches for Atomisation’

coffee break

17:00–18:30: Greg Restall (University of St Andrews), ‘: Relating Constructive, Classical and Substructural Logics’

aperitif and dinner

FUNDING AND REGISTRATION:

The workshop is organised by Carlos Benito, Bogdan Dicher and Elia Zardini and funded by the FCT Project *New Perspectives on the Objects and Grounds of Structural Rules*. There are no registration fees, but if you would like to attend please let Carlos Benito know at carlos.b.21@hotmail.com