A hierarchy of dependencies

0534292 - FLÚ 2021 FI eng C - Conference Paper (international conference)
Punčochář, Vít
A hierarchy of dependencies.
Proceedings of Workshop on Logics of Dependence and Independence (LoDE 2020V). Helsinki: University of Helsinki, Department of Mathematics and Statistics, 2020 - (Väänänen, J.; Yang, F.), s. 32-36. Acta generalia instituti mathematico-rationarii.
[Workshop on Logics of Dependence and Independence (LoDE 2020V). Online, 10.08.2020-12.08.2020)]
R&D Projects: GA ČR(CZ) GA20-18675S
Institutional support: RVO:67985955
Keywords : dependence logic * contexts * non-classical logics * conditionals
OECD category: Philosophy, History and Philosophy of science and technology
http://hdl.handle.net/10138/317202

Semantic frameworks are commonly based on the notion of truth that is captured as a relation between possible worlds and formulas. The team semantics for propositional dependence logic (Yang and Va ̈a ̈na ̈nen 2016, 2017) is based on the observation that propositional dependence cannot be defined in terms of truth relative to single possible worlds. Above the layer of possible worlds, one needs to add the extra layer of teams (sets of possible worlds) and define dependency relations among statements relative to these teams. We have here an example of a peculiar semantic relativity: While atomic statements are primarily evaluated with respect to possible worlds, dependence statements are primarily evaluated with respect to teams. This paper is motivated by the view that this kind of relativity is a more integral part of language than it might seem and in order to capture it in full generality one should go beyond the two-layered framework (involving just possible worlds and sets of possible worlds) and employ a whole hierarchy of other types of semantic objects. These new semantic objects allow us to capture higher-order dependencies as well as some tricky interaction between the dependence operator and other logical operators.
Permanent Link: http://hdl.handle.net/11104/0312516