LLAL@GSIS (II)

Date & Venue

• Date: March 9, 2024.

• Venue: Room 609, Graduate School of Information Sciences, Tohoku University.  

Speakers

• Rohan French (UC Davis)

• Andrzej Indrzejczak (University of Łódź)

• Nils Kürbis (Ruhr University Bochum and University of Łódź)

• Shawn Standefer (National Taiwan University)

Program

13:00--14:15 Shawn Standefer "Universal necessity and Scroggs properties"

14:15--15:30 Rohan French "What is a Constructive Paraconsistent Logic?"

15:30--15:45 Break

15:45--17:00 Nils Kürbis "Some Systems for Formalising Definite Descriptions with a Binary Quantifier in Free Logic"

17:00--18:15 Andrzej Indrzejczak "Application of Bisequent Calculus to Neutral Free Logic with Definite Descriptions"

Abstracts

Shawn Standefer: The universal conception of necessity says that necessary truth is truth in all possible worlds. This idea is well studied in the context of classical possible worlds models, and there its logic is S5. This notion of necessity is less well studied in non-classical models, and depending on the logic may differ from that of S5. One of the major results about S5 is due to Scroggs. Scroggs provided a neat characterization of all proper extensions of S5 and showed that they all have finite characteristic matrices. We will present some preliminary results on universal necessity in models for relevant logics and for intuitionistic logic. We will discuss some possible avenues for theorems like those of Scroggs. (This is a joint work with Rohan French.)

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Rohan French: In this paper I’ll discuss a constructive logic which stands to LP just as intuitionistic logic stands to classical logic, and show the completeness of its conservative extension with an operator representing the notion of a sentence being ‘strictly true’ or ‘just true’, reflecting on the conceptual and technical issues this raises..

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Nils Kürbis: In this talk I’ll present a number of systems for formalising complete sentences in which definite descriptions occur, `The F is G’, with a binary quantifier as Ix(F, G). I’ll present the systems in natural deduction, but they also have equivalent formulations in sequent calculus. The first system is suitable for negative free logic. The characteristic of negative free logic is that atomic propositions in which non-referring terms occur cannot be true. Correspondingly, Ix(F, G) won’t be true if there is no unique F. The result is Russellian: 'The F is G' is equivalent to the Russellian analysis of such sentence: there is exactly one F and it is G. I briefly compare this system with a system of Tennant's in which definite descriptions are formalised as singular terms by a term forming operator. The rules for I could also be added to positive free logic. However, the characteristic of positive free logic is that sentences containing non-referring terms can be true, and analogously, it should be possible for `The F is G’ to be true even if no unique F exists. In a second system, I present rather complicated rules for I that were motivated by exactly this consideration. In a third system, I present drastically simplified rules, also for positive free logic, which I propose as a new theory of definite descriptions in positive free logic. I compare it briefly with standard approaches to the formalisation of definite descriptions in positive free logic as singular terms.

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Andrzej Indrzejczak: We present a bisequent calculus (BSC) for the minimal theory of definite descriptions (DD) in the setting of neutral free logic, where formulae with non-denoting terms have no truth value. The treatment of quantifiers, atomic formulae and simple terms is based on the approach developed by Pavlovic and Gratzl. We extend their results to the version with identity and definite descriptions. In particular, the admissibility of cut is proven for this extended system. (This is a joint work with Yaroslav Petrukhin.)