Title: A complete logic for first-order team properties

Speaker: Fan Yang (Utrecht University)

Time: 2024/04/01 15:10-18:00

Location: Room B112, Lee Shau Kee Humanities Buildings No.2 (李兆基人文学苑2号楼), Peking University

Abstract:
　　Team semantics is a semantical framework originally introduced by Hodges [1], and later further refined by by Väänänen [4] with the introduction of dependence logic, which is a proper extension of first-order logic with dependence atoms. The strong expressive power of dependence logic makes it impossible to provide complete axiomatization of the logic. Finding weaker and axiomatizable fragment or variants of dependence logic is thus a main challenge in the field. In [1] Baltag and van Benthem introduced an axiomatizable and decidable logic of dependence building on a variant of team semantics. In this talk, we discuss a different axiomatizable variant of dependence logic, called FOT, defined by incorporating weaker connectives and quantifiers to the original team semantics. We show that FOT captures all first-order definable team properties, and thus can be viewed as the first-order logic of team semantics. We also discuss (potential) applications of FOT.

　　This talk is based on [3].

References:

[1] Baltag and van Benthem, A simple logic of functional dependence, Journal of Philosophical Logic, vol. 50 (2021), no. 5, pp. 939–1005.

[2] Hodges, Compositional semantics for a language of imperfect information, Logic Journal of the IGPL, vol. 5 (1997), pp. 539–563.

[3] Kontinen and Yang, Complete logics for elementary team properties, Journal of Symbolic Logic, Volume 88, Issue 2, June 2023, pp. 579-619.

[4] Väänänen, Dependence logic: A new approach to independence friendly logic, Cambridge University Press, 2007.