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Foundations
I shall set up the basic framework in three steps. First, in Section 1.1, I shall introduce the notion of a language, regarded as a purely...
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An Equational Axiomatization of Dynamic Negation and Relational Composition
We consider algebras on binary relations with two main operators: relational composition and dynamic negation. Relational composition has its...
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Modal Logics of Relations
In other chapters we have seen or will see how logics from various origins can be treated in the unifying framework of multi-dimensional modal logic....
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Logics of Schemes for First-Order Theories and Poly-Modal Propositional Logic
Schemes of theorems are a well-known object of study in logic; general properties of first-order theories are expressible exactly by formula schemes....
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Multi-Dimensional Modal Logic
We start with informally defining the subject matter of this book: multi-dimensional modal logic (MDML). First let us briefly consider what we...
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The Prehistory of Infinitary Logic: 1885–1955
Traditionally, logic was restricted to proofs having a finite number of steps and to expressions of finite length. Around 1954–56, infinitely long...
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Modal Logics of Arrows
There exist many formal schemes and tools for representing knowledge about different types of data. Sometimes we can gain a better understanding if...
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Logic in Central and Eastern Europe: Balkan Region
The main aim of this lecture is to give some information about Logic in the Balkan region before and after the collapse of the communist system. In...
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Two-Dimensional Modal Logics
This chapter contains a technical introduction to the world of multi-dimensional modal logics. We will treat some relatively simple logics with a...
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Modal Quantification over Structured Domains
The semantics for quantifiers described in this paper can be viewed both as a new semantics for generalized quantifiers and as a new look at standard...
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Free Q-distributive lattices
The dual spaces of the free distributive lattices with a quantifier are constructed, generalizing Halmos' construction of the dual spaces of free...
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Gabbay-Style Calculi
It is well known that there are logics, e.g. classical first-order logic with n variables, ℒ n , that do not have...
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Relational Proof Systems for Modal Logics
The purpose of this paper is to give a survey of the relational formalization of modal logics. The paradigm ‘formulas are relations’ leads to the...
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Sahlqvist's theorem for boolean algebras with operators with an application to cylindric algebras
For an arbitrary similarity type of Boolean Algebras with Operators we define a class of Sahlqvist identities . Sahlqvist identities have two important...