[logic-ml] The second「論数哲」(PhilLogMath) workshop

[Shunsuke Yatabe]

The second「論数哲」"Ron-Suu-Tetsu" (PhilLogMath) workshop

We will hold the 2nd 「論数哲」(PhilLogMath) workshop. Our aim is to provide 
opportunities of detailed discussions among philosophers, logicians and 
mathematicians. Everyone is welcome.

     website url:  http://researchmap.jp/jovzjd6b4-21098/#_21098

     Date :  March 14 (Wed)
     Place:  Seiryo Kaikan (Nagata-cho, Tokyo) Room 4A and 4B (floor 4)
		http://metropolis.co.jp/listings/venues/type/stage-venue/seiryo-kaikan/
     Time table
         9:00-10:30  Takuro Onishi  (Kyoto University)  "BHK-interpretation 
and Bilateralism"
         10:30-12:00 Katsuhiko Sano (JAIST)
					"An `Impossibility' Theorem in Radical  Inquisitive Semantics"
         13:30-15:00 Masahiko Sato (Kyoto University) "Bootstrapping 
Mathematics"
         15:15-16:45 Richard Dietz  (The University of Tokyo)  "Comparative 
Concepts"
         17:00-18:30 Conrad Asmus (JAIST) " Vagueness and Revision Sequences"

Any slot consists of 60 minutes talk and 30 minutes discussion basically.
All talks are in English.

Abstracts:
* Takuro Onishi "BHK-interpretation and Bilateralism"
In this talk, H.Wansing's inferentialist semantics for Bi-intuitionist logic 
is examined.Bi-intuitionist Logic (a.k.a. Heyting-Brouwer logic) is an 
extension of Intuitionist Logic with a connective dual to implication. It is 
sort of an amalgamation of intuitionist and dual-intuitionist logic. 
Accordingly, BHK-like, inferentialist, or proof-theoretic semantics for the 
logic would be a bilateralist one appealing to not only "proof" but 
also"dual proof (disproof)" as primitive notions. In his "Proofs,disproofs 
and their duals" (2010),Wansing gives a correctness (soundness) proof of a 
display system for bi-intuitionist logic in terms of the bilateralist 
semantics. I point out that his proof involves controversial assumptions 
concerning the relation between proofs and dual proofs and present an 
alternative view on how they get together. (Although Wansing discuss a 
BHK-like interpretation for strong negation and its dual as well, I will 
concentrate on logics without them in this talk.)

*Katsuhiko Sano "An `Impossibility' Theorem in Radical  Inquisitive Semantics"
An aim of this talk is to show that it is impossible to provide a `natural' 
Kripke semantics with radical inquisitive semantics, recently proposed by 
Jeroen Groenendijk and Floris Roelofsen. Inquisitive semantics is a new 
formal framework for the semantics of both declarative and interrogative 
sentences. One of the main features of this semantics is that we assume 
there is no type distinction between the declarative and the interrogative, 
but we provide both classical and inquisitive meanings with each sentence. 
For example, the declarative sentence `Taro will drink tea or coffee.' 
proposes two alternatives `Taro will drink tea' and `Taro will drink 
coffee'. Inquisitive meaning captures such information of the alternatives. 
In conservative (non-radical) inquisitive semantics (Groenendijk and 
Roelofsen 2009), intuitionistic Kripke semantics captures how our group 
knowledge increases though a conversation, and also allows us to derive the 
inquisitive meaning of a sentence from the classical meaning. In the example 
above, we could give a reply `Taro won't drink tea or coffee' to the 
speaker. In conservative inquisitive semantics, however, we cannot cover 
such a negative reaction. Radical inquisitive semantics is an extension of 
conservative one such that we can provide with each sentence the positive 
and negative inquisitive meanings as well as the classical meaning. My 
contribution of this talk is to establish that *any* `natural' Kripke 
semantics fails to capture a link between the classical meaning and the 
negative inquisitive meaning.

*Masahiko Sato "Bootstrapping Mathematics"
It is well-known that any formal mathematical system can be faithfully 
encoded within PRA (Primitive Recursive Arithmetic). It is also commonly 
accepted that any well-established part of mathematics can be presented as a 
formal system. Thus, it seems that we can bootstrap mathematics, within a 
computer, simply by implementing PRA in it. However, we will show that this 
view is too naiive both from computer science point of view and from 
foundational point of view. We also discuss an alternative approach to this 
problem by giving an overview of a proof assistant system we are developing.

*Richard Dietz "Comparative Concepts"
Comparative concepts (such as ‘greener than’ or ‘higher than’)are 
fundamental to our grasp of associated categorical concepts (‘green’, 
‘high’, respectively). Some comparative concepts seem natural, whereas other 
ones seem rather gerrymandered---e.g., compare ‘x is greener than y’ and ‘x 
and y are such that either (i) x and y are inspected before midday and x is 
greener than y, or (ii) x and y are inspected after midday and x is bluer 
than y’. What kind of cognitive structures under your ability to order 
objects? And why do we order objects the way we do,and not in other ways? 
The aim of this talk is to outline an account of comparative concepts within 
a conceptual spaces framework. The account bears for one on the account of 
naturalness for comparative concepts.For another, it bears on the theory of 
gradable concepts, i.e., the type of categorical concepts expressed by 
gradable terms in natural language.The approach is novel in that it carries 
some basic assumptions from Peter Gärdenfors' conceptual spaces account of 
categorical concepts over to comparative concepts (in his monograph 
‘Conceptual Spaces’ [2000]).The offered approach is more general both (i) in 
that it supplies a framework for motivating various types of categorisation 
rules for gradable concepts, and (ii) in that it gives a model that subsumes 
ungraded categorisation as a limiting case.

*Conrad Asmus "Vagueness and Revision Sequences"
Theories of truth and vagueness are closely connected; in this article, I 
draw another connection between these areas of research. Gupta and Belnap’s 
Revision Theory of Truth is converted into an approach to vagueness. I show 
how revision sequences from a general theory of definitions can be used to 
understand the nature of vague predicates. The revision sequences show how 
the meaning of vague predicates are interconnected with each other. The 
approach is contrasted with the similar supervaluationist approach.

*Workshop organizer (please replace [at] to @):
         Yuko Murakami
         Shunsuke Yatabe ( shunsuke.yatabe[at]aist.go.jp )
         Takuro Onishi ( takuro.onishi[at]gmail.com )

-- 
Shunsuke Yatabe <shunsuke.yatabe at aist.go.jp>
AIST/CVS (National Institute of Advanced Industrial Science and Technology /
         Research Center for Verification and Semantics)
tel: +81-6-4863-5031   fax: +81-6-4863-5052