0 Intuitionistic modal logics originate from di erent sources and have di erent areas of application. They include philosophy (see e.g. Prior [1957], Ewald [1986], Williamson [1992]), the foundations of mathematics (Kuznetsov [1985], Kuznetsov and Muravitskij [1986]), and computer science (Plotkin and Stirling [1986], Stirling [1987], Wijesekera [1990]). Modalities are added to intuitionistic l...

The decidability of multiplicative exponential linear logic (MELL) is currently open. I show that two independently interesting refinements of MELL that alter only the syntax of proofs—leaving the underlying truth untouched— are undecidable. The first refinement uses new modal connectives between the linear and the unrestricted judgments, and the second is based on focusing with priority assign...

We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal propositional logic FPL, and Jankov’s logic KC. We show that the model checking problem is P-complete for the implicational fragments of all these intuitionistic log...

Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary predicate symbols. Monadic second order logic over infinite words (S1S) can alternatively be described as a first-order logic interpreted in P(ω), the power set...

We propose a general and uniform modal framework for the Event Calculus (EC) and its skeptical and credolous variants. The resulting temporal formalism, called the Generalized Modal Event Calculus (GMEC), extends considerably the expressive power of EC when information about the ordering of events is incomplete. It provides means of inquiring about the evolution of the maximal validity interval...

This paper presents a recent formalization of Henkin-style completeness proof for the propositional modal logic S5 using Lean theorem prover. The formalized is close to that Hughes and Cresswell [], but system, based on different choice axioms, better described as Mendelson system augmented with axiom schemes K, T, S4, B, necessitation rule inference. language has false implication only primiti...

In the present paper, we propose Abstract Algebraic Logic (AAL) as a general logical framework for Judgment Aggregation. Our main contribution is a generalization of Herzberg’s algebraic approach to characterization results on judgment aggregation and propositionalattitude aggregation, characterizing certain Arrovian classes of aggregators as Boolean algebra and MV-algebra homomorphisms, respec...

In the present paper, we propose Abstract Algebraic Logic (AAL) as a general logical framework for Judgment Aggregation. Our main contribution is a generalization of Herzberg’s algebraic approach to characterization results in on judgment aggregation and propositionalattitude aggregation, characterizing certain Arrovian classes of aggregators as Boolean algebra and MV-algebra homomorphisms, res...