12 research outputs found
Interplays of knowledge and non-contingency
This paper combines a non-contingency logic with an epistemic logic by means of fusions and products of modal systems. Some consequences of these interplays are pointed out
Neighbourhood contingency bisimulation
We introduce a notion of bisimulation for contingency logic interpreted on neighbourhood structures, characterise this logic as bisimulation-invariant fragment of modal logic and of first-order logic, and compare it with existing notions in the literature
S5-Style Non-Standard Modalities in a Hypersequent Framework
The aim of the paper is to present some non-standard modalities (such as non-contingency, contingency, essence and accident) based on S5-models in a framework of cut-free hypersequent calculi. We also study negated modalities, i.e. negated necessity and negated possibility, which produce paraconsistent and paracomplete negations respectively. As a basis for our calculi, we use Restall's cut-free hypersequent calculus for S5. We modify its rules for the above-mentioned modalities and prove strong soundness and completeness theorems by a Hintikka-style argument. As a consequence, we obtain a cut admissibility theorem. Finally, we present a constructive syntactic proof of cut elimination theorem
Knowledge and ignorance in Belnap--Dunn logic
In this paper, we argue that the usual approach to modelling knowledge and
belief with the necessity modality does not produce intuitive outcomes
in the framework of the Belnap--Dunn logic (, alias
-- first-degree entailment). We then motivate and introduce a non\-standard
modality that formalises knowledge and belief in
and use to define and that
formalise the \emph{unknown truth} and ignorance as \emph{not knowing whether},
respectively. Moreover, we introduce another modality that stands
for \emph{factive ignorance} and show its connection with .
We equip these modalities with Kripke-frame-based semantics and construct a
sound and complete analytic cut system for and
-- the expansions of with
and . In addition, we show that as it is customarily defined
in cannot define any of the introduced modalities, nor,
conversely, neither nor can define . We also
demonstrate that and are not interdefinable and
establish the definability of several important classes of frames using
Achieving while maintaining:A logic of knowing how with intermediate constraints
In this paper, we propose a ternary knowing how operator to express that the
agent knows how to achieve given while maintaining
in-between. It generalizes the logic of goal-directed knowing how proposed by
Yanjing Wang 2015 'A logic of knowing how'. We give a sound and complete
axiomatization of this logic.Comment: appear in Proceedings of ICLA 201