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 investigates (modal) extensions of Heyting-Brouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We rst develop matrix as well as Kripke style semantics for those logics. Then, by extending the Godel-embedding of intuitionistic logic into S4, it is shown that all (modal) extensions of Heyting...

We introduce a class of algebras, called twist-structures, whose members are built as special squares of an arbitrary residuated lattice. We show how our construction relates to and encompasses results obtained by several authors on the algebraic semantics of non-classical logics. We define a logic that corresponds to our twist-structures and show how to expand it with modal operators, obtainin...

Adam Brandenburger and H. Jerome Keisler have recently discovered a two person Russell-style paradox. They show that the following configurations of beliefs is impossible: Ann believes that Bob assumes that Ann believes that Bob’s assumption is wrong. In [7] a modal logic interpretation of this paradox is proposed. The idea is to introduce two modal operators intended to represent the agents’ b...

This paper proposes a modal logic reconstruction of temporal reasoning about partially ordered events in a logic programming framework. It considers two variants of Kowalski and Sergot's Event Calculus (EC): the Skeptical EC (SKEC) and the Credulous EC (CREC). In the presence of partially ordered sequences of events, SKEC and CREC derive the maximal validity intervals over which the relevant pr...

Five algebraic notions of termination are formalised, analysed and compared: well-foundedness or Noetherity, Löb’s formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings, which are additively idempotent semirings with forward and backward modal operators. To reason about infinite behaviour, semirings are extended to divergence semi...

We introduce a modal language L which is obtained from standard modal logic by adding the Boolean operators on accessibility relations, the identity relation, and the converse of relations. It is proved that L has the same expressive power as the two-variable fragment FO of first-order logic, but speaks less succinctly about relational structures: if the number of relations is bounded, then L-s...

The article introduces a ceteris paribus modal logic interpreted on the equivalence classes induced by sets of propositional atoms. This logic is used to embed two logics of agency and games, namely atemporal STIT and the coalition logic of propositional control (CL−PC). The embeddings highlight a common ceteris paribus structure underpinning the key modal operators of both logics, they clarify...

Granular reasoning proposed by Murai et al. is a mechanism for reasoning using granular computing, and the concept of “focus” has been proposed as a key concept of granular reasoning. On the other hand, the authors have proposed another concept of granularity, called “visibility”. In this paper, we try to capture the concepts of visibility and focus as modalities of modal logics by introducing ...

in terms of de dicto necessity, necessity conceived as a property of propositions or sentences. The heart of Plantinga's theory is his scheme for the reduction of de re modal sentences to equivalent de dicto ones. The idea is to provide an equivalent sentence containing no modal operators within the scope of a quantifier for every sentence asserting that some thing is necessarily or essentially...