Towards a natural language semantics without functors and operands
The paper sets out to offer an alternative to the function/argument approach to the most essential aspects of natural language meanings. That is, we question the assumption that semantic completeness (of, e.g., propositions) or incompleteness (of, e.g., ...
A Hybrid Logic for Reasoning about Knowledge and Topology
We extend Moss and Parikh's bi-modal system for knowledge and effort by means of hybrid logic. In this way, some additional concepts from topology related to knowledge can be captured. We prove the soundness and completeness as well as the decidability ...
First-Order Glue
Glue has evolved significantly during the past decade. Although the recent move to type-theoretic notation was a step in the right direction, basing the current Glue system on System F (second-order -calculus) was an unfortunate choice. An extension to ...
Strong Completeness and Limited Canonicity for PDL
Propositional dynamic logic ($$\mathsf{PDL}$$) is complete but not compact. As a consequence, strong completeness (the property $$\Gamma \models \varphi \Rightarrow \Gamma \vdash \varphi$$) requires an infinitary proof system. In this paper, we present ...
The basic constructive logic for a weak sense of consistency
In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic B Kc1 adequate to this sense of consistency in the ternary ...
On combinations of propositional dynamic logic and doxastic modal logics
We prove completeness and decidability results for a family of combinations of propositional dynamic logic and unimodal doxastic logics in which the modalities may interact. The kind of interactions we consider include three forms of commuting axioms, ...