**August 2022**

IIF-SADAF-CONICET

Buenos Aires, Argentina

Sara Ayhan (Ruhr-Universität Bochum, Germany)

Katalin Bimbo (University of Alberta, Canada)

Bogdan Dicher (University of Lisbon, Portugal)

**Tuesday 09**

14:30 to 19:10 (GMT-03)

(14:30 – 15:40) Bruno Da Ré and Damián Szmuc: “Cut-free sequent-calculi for classical logic”

(16:00 – 17:10) Miguel Álvarez Lisboa: “The invalidities of intuitionistic logic”

(18:00 – 19:10) Sara Ayhan: “Meaning and identity of proofs in a bilateralist setting: A two-sorted typed λ-calculus for 2Int”

**Friday 12**

14:30 to 19:10 (GMT-03)

(14:30 – 15:40) Mariela Rubin: “Three-valued conditionals: interpreting its truth table”

(16:00 – 17:10) Camillo Fiore: “Reading Conclusions Conjunctively”

(18:00 – 19:10) Bogdan Dicher: “Remarks on dual-intuitionistic logic”

**Friday 19**

17:30 to 19:00 (GMT-03)

(17:30 – 19:00) Katalin Bimbo: “Some sequent calculuses for some relevance logics”

**Bruno Da Ré and Damián Szmuc: “Cut-free sequent-calculi for classical logic”**

The aim of this talk is to present an algorithmic method to determine, given a cut-free sequent calculus, if it is sound and complete for classical logic.

**Miguel Álvarez Lisboa: “The invalidities of intuitionistic logic”**

Those who work on compared logics know that sometimes a precise characterization of what logics invalidate may be just as important as a characterization of what they validate. This is true, in particular, in the case of intuitionistic logic (IL) and its arch-nemesis, classical logic (CL), where our understanding of their difference can be easily misguided by imprecise slogans. Regarding CL, some calculi of its invalidities have been provided already in the literature. But for the former, as far as I know, they are still lacking. In this talk I fill in this gap with a sequent calculus for the invalidities of IL. I also provide a first comparison between these and the invalidities of CL. Some insights of philosophical relevance will be highlighted, in the hope that these may help us better understand the subtle differences between two well-known rival logics.

**Sara Ayhan: “Meaning and identity of proofs in a bilateralist setting: A two-sorted typed λ-calculus for 2Int”**

In this talk I want to present some work in progress which is meant to connect certain ideas on meaning and reference of proofs, spelled out in (Ayhan, 2021) and (Tranchini, 2016), with a bilateralist program in proof-theoretic semantics, taking proofs and refutations on a par- For this I will consider the bi-intuitionistic logic 2Int, which represent a specific form of bilateralism in that it exhibits two derivability relations, one for verification and one for falsification (cf. Wansing (2016), Wansing (2017) and Ayhan (2020)).

I will present a two-sorted typed λ-calculus for this logic and point out some peculiarities of that calculus. Finally, I want to shear some ideas on how we can use such a system if we are interested in questions about references, meaning, identity and synonymy of proofs. If we want to consider a bilateralist standpoint in these questions, this approach might give us some interesting answers in that it yields the desired balance between proofs and refutations both being primitive.

**Mariela Rubin: Three-valued conditionals: interpreting its truth table**

The aim of this work is to defend a three-valued semantics to model the behavior of the indicative conditional based on the truth tables and the probabilistic calculus originally proposed by De Finetti in 1936. Yet, I will defend, in line with Adams (1965, 1975), Edgington (1995) and Bennett (2003), that indicative conditional does not express a proposition, but the degree of confidence in the consequent in case the antecedent happens to be true. The main thesis to defend is that De Finetti’s proposal implies a non-propositional reading of the conditional, although the literature that followed him interpreted it oppositely. At the same time, I will argue that the non-propositional reading of the indicative conditional is not only compatible with this trivalued semantic but it also allows the thesis to enrich its syntax and semantics by allowing conditionals to be sub-formulas of any formula of the language.

**Camillo Fiore: “Reading Conclusions Conjunctively”**

Since Gentzen’s seminal works on proof theory, it has slowly become widespread to work with logical systems where arguments can have multiple conclusions. In philosophical logic, the mainstream is to assume a disjunctive reading of conclusions: Γ entails &\Delta; just in case Γ entails the disjunction of the things in &\Delta; (where Γ and &\Delta; are collections of the appropriate kind). An alternative approach would be to assume a conjunctive reading: Γ entails &\Delta; just in case Γ entails the conjunction of the things in &\Delta;. It is remarkable that, while this latter approach is common currency in algebraic logic, it has gone largely unnoticed by philosophers. My aim in this paper is to start reversing this situation. First, I show how to apply the conjunctive reading of multiple conclusions to first-order classical logic, both from a model-theoretic and a proof-theoretic perspective. Then, I give a series of reasons why this reading can be regarded of significant philosophical interest.

**Bogdan Dicher: “Remarks on dual-intuitionistic logic”**

Dual-intuitionistic logic is a substructural logic whose sequent calculus presentation allows (at most) singleton antecedents, just like usual sequent calculus presentations of intuitionistic logic have (at most) singleton succedents. In this talk I will provide an analysis of dual-intuitionsitic logic seen as consequence relation on sequents rather than formulae.

**Katalin Bimbo: “Some sequent calculuses for some relevance logics”**

The conditional of classical logic and the implication of intuitionistic logic are residuals of their respective conjunction connectives. The implications of relevance logics are not residuals of (extensional) conjunction. Sequent calculuses for a relevance logic cannot contain unrestricted weakening, because that would allow a proof of the positive paradox. I will present several sequent calculuses (some older and some newer) and highlight some crucial ideas together with connections to sequent calculuses for other logics.

We are thankful for the support provided by CONICET and MINCYT