This paper studies a particular interpretation of propositional modal logic into propositional modal logic. Under an epistemic reading of the modality this interpretation can be understood as taking knowledge to be true belief. All normal modal logics of belief that under this definition of knowledge give rise to S5 as the logic of knowledge are determined. And all the normal modal logics of be...

Various logic-based frameworks have been proposed for specifying the operational semantics of programming languages and concurrent systems, including inference systems in the styles advocated by Plotkin and by Kahn, Horn logic, equational specifications, reduction systems for evaluation contexts, rewriting logic, and tile logic. We consider the relationship between these frameworks, and assess ...

We discuss a formal many-valued logic called EQlogic which is based on a recently introduced special class of algebras called EQ-algebras. The latter have three basic binary operations (meet, multiplication, fuzzy equality) and a top element and, in a certain sense, generalize residuated lattices. The goal of EQ-logics is to present a possible direction in the development of mathematical logics...

We investigate how abduction and induction can be integrated into a common learning framework through the notion of Abductive Concept Learning (ACL). ACL is an extension of Inductive Logic Programming (ILP) to the case in which both the background and the target theory are abductive logic programs and where an abductive notion of entailment is used as the coverage relation. In this framework, i...

For a cardinal of the form κ = בκ, Shelah’s logic L 1 has characterisation as maximal above $${ \cup _{\lambda < \kappa }}{L_{\lambda ,\omega }}$$ satisfying strengthening undefinability well-order. Karp’s chain [20] is known to satisfy well-order and interpolation. We prove that if singular countable cofinality, . Moreover, we show strong limit cardinals $$L_{ , }^c{ }}L_{\lambda ,\lambda }^c$...

Abstract We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic ( $$\textrm{CHL}$$ CHL ), hereby introduced as an example of a strongly connexive with intuitive semantics. use the reverse algebraisation paradigm: presented assertional point regular variety (whose structur...

Most of the work on inheritance hierarchies in recent years has had as its goal the design of general purpose algorithms that depend only on the topology of the inheritance network. This research has produced some important observations about the various strategies used in human common sense reasoning, but it has also produced a proliferation of incompatible systems. In this paper, we resurrect...