This paper offers a semantic study in multi-relational semantics of quantified N-Monotonic modal logics with varying domains with and without the identity symbol. We identify conditions on frames to characterise Barcan and Ghilardi schemata and present some related completeness results. The characterisation of Barcan schemata in multi-relational frames with varying domains shows the independence of BF and CBF from well-known propositional modal schemata, an independence that does not hold with constant domains. This fact was firstly suggested for classical modal systems (...) by Stolpe, 557–575, 2003), but unfortunately that work used only models and not frames. (shrink)

A number of significant contributions in the last four decades show that non-normal modal logics can be fruitfully employed in several applied fields. Well-known domains are epistemic logic, deontic logic, and systems capturing different aspects of action and agency such as the modal logic of agency, concurrent propositional dynamic logic, game logic, and coalition logic. Semantics for such logics are traditionally based on neighbourhood models. However, other model-theoretic semantics can be used for this purpose. Here, we systematically study multi-relational structures, (...) whose investigation is still relatively underdeveloped. After a brief introduction to two different versions of multi-relational semantics – which we call strong and weak multi-relational semantics – we proceed to study several modal schemata. Special attention is paid to the schemata CON and D. Finally we offer completeness proofs for several systems using both strong and weak semantic tools: The proofs thus cover both classical system.. (shrink)

The paper aims at providing the multi-modal propositional logic LTK with a sound and complete axiomatisation. This logic combines temporal and epistemic operators and focuses on m odeling the behaviour of a set of agents operating in a system on the background of a temporal framework. Time is represented as linear and discrete, whereas knowledge is modeled as an S5-like modality. A further modal operator intended to represent environment knowledge is added to the system in order to achieve the expressive (...) power sufficient to describe the piece of information available to the agents at each moment in the flow of time. (shrink)

The paper investigates admissible inference rules for the multi-modal logic LTK, which describes a combination of linear time and knowledge. This logic is semantically defined as the set of all ℒ.