De Re Updates

In this paper, we propose a lightweight yet powerful dynamic epistemic logic that captures not only the distinction between de dicto and de re knowledge but also the distinction between de dicto and de re updates. The logic is based on the dynamified version of an epistemic language extended with the assignment operator borrowed from dynamic logic, following the work of Wang and Seligman (Proc. AiML 2018). We obtain complete axiomatizations for the counterparts of public announcement logic and event-model-based DEL based on new reduction axioms taking care of the interactions between dynamics and assignments.Comment: In Proceedings TARK 2021, arXiv:2106.1088

Non-Rigid Designators in Epistemic and Temporal Free Description Logics (Extended Version)

Definite descriptions, such as 'the smallest planet in the Solar System', have been recently recognised as semantically transparent devices for object identification in knowledge representation formalisms. Along with individual names, they have been introduced also in the context of description logic languages, enriching the expressivity of standard nominal constructors. Moreover, in the first-order modal logic literature, definite descriptions have been widely investigated for their non-rigid behaviour, which allows them to denote different objects at different states. In this direction, we introduce epistemic and temporal extensions of standard description logics, with nominals and the universal role, additionally equipped with definite descriptions constructors. Regarding names and descriptions, in these languages we allow for: possible lack of denotation, ensured by partial models, coming from free logic semantics as a generalisation of the classical ones; and non-rigid designation features, obtained by assigning to terms distinct values across states, as opposed to the standard rigidity condition on individual expressions. In the absence of the rigid designator assumption, we show that the satisfiability problem for epistemic free description logics is NExpTime-complete, while satisfiability for temporal free description logics over linear time structures is undecidable

Free Quantified Epistemic Logics

The paper presents an epistemic logic with quantification over agents of knowledge and with a syntactical distinction between de re and de dicto occurrences of terms. Knowledge de dicto is characterized as `knowledge that', and knowlegde de re as `knowledge of'. Transition semantics turns out to be an adequate tool to account for the distinctions introduced