Vita Saitta

In the last few decades, truthmaker semantics has attracted the attention of scholars from various areas, arguably due to its philosophical underpinning and its flexibility in addressing a number of problems that are difficult to solve using alternative semantic frameworks. Attention is now focused on developing truthmaker semantics for modal logic; this paper contributes to that direction. The basic idea we introduce is that truthmakers of modal sentences are norms. This allows us to derive two interesting results: first, we introduce a new modal semantics for minimal monotonic logic; second, we provide a truthmaker semantics for every modal logic characterized by a class of Kripke frames. This is, as far as we can tell, the first general result about truthmaker semantics for normal modal logics.

This paper introduces a new framework, based on the notion of compatibility space, obtained by adding a primitive incompatibility relation to a state space in the sense of Fine. The key idea inspiring the framework is to modify Fine's truthmaker semantics by taking the notion of incompatibility as primitive, and use it to define other notions. We discuss some interesting features of the framework and explore its advantages over the standard framework of state spaces. We review some applications of the framework, including proofs of soundness and completeness theorems for a number of logics, one way to use compatibility states to mirror Kripke frames, and an exploration of a way to use the new framework to provide truthmaking clauses for modal formulas.

The aim of this work is to investigate the problem of Logical Omniscience in epistemic logic by means of truthmaker semantics. We will present a semantic framework based on $$\varvec{W}$$ W -models extended with a partial function, which selects the body of knowledge of the agents, namely the set of verifiers of the agent’s total knowledge. The semantic clause for knowledge follows the intuition that an agent knows some information $$\varvec{\phi }$$ ϕ, when the propositional content that $$\varvec{\phi }$$ ϕ is contained in her total knowledge. We will argue that this idea mirrors the philosophical conception of immanent closure by Yablo (2014), giving to our proposal a strong philosophical motivation. We will discuss the philosophical implications of the semantics and we will introduce its axiomatization.