西溪逻辑论坛第62期

Speaker: Dr. Junhua Yu
Date & Time: 14 April 2017 (Friday), 13:30 – 15:00
Place: Seminar room #259, Main teaching building, Xixi campus, Zhejiang University

Abstract:

S. Artemov’s justification logic (JL) can be seen as an explicit version of modal logic (ML). Instead of modality \Box, JL has inductively defined terms in its language, and formula t:\phi means term t is a justification of formula \phi. The formal link between ML and JL is called ‘realization’, via which ML’s get their ‘constructive semantics’. A realization of a ML-theorem \phi is a theorem in the corresponding JL gained by carefully replace each occurrence of \Box in \phi by an appropriate JL-term that reveals the hidden constructive meaning of the replaced \Box-occurrence. R. Kuznets showed that self-referential JL-formulas of the form t:\phi(t) are necessary in realizing several ML’s including S4, via which intuitionistic propositional logic IPC receives its provability BHK-interpretations in Godel-Artemov approach.. In this talk, the speaker will present several results he got in recent years concerning image of self-referentiality on the modal and propositional layer.

Slides

References:

Junhua Yu: Self-referentiality of Brouwer–Heyting–Kolmogorov semantics. APAL 165(1) 371–388 (2014).
Junhua Yu: On non-self-referential fragments of modal logics. APAL 168(4) 776–803 (2017).

（本活动受中央高校基本科研业务费专项资金资助）