There is a natural way to add rules for rst-order quanti ers to proof theories for propositional relevant logics, and there is a natural way to add evaluation conditions for quanti ers to the semantics for propositional relevant logics. Kit Fine has shown us that these two natural ways of modelling rst order relevant logics do not match up [6]. Furthermore, Fine has given a semantics for the na...

We present an approach to providing natural deduction style proof systems for a large class of quantiied modal logics with varying, increasing, decreasing or constant domains of quantiication. The systems we develop are modular both in the behavior of the accessibility relation and quantiication relative to the semantics, and in the proofs of soundness and completeness relative to that semantic...

This paper discusses advantages and disadvantages of some possible alternatives for inference rules that handle quanti ers in the proof format of the SMT-solver veriT. The quanti erhandling modules in veriT being fairly standard, we hope this will motivate the discussion among the PxTP audience around proof production for quanti er handling. This could generate ideas to help us improve our proo...

We consider an extension of the mu-calculus as a general framework to describe and synthesize controllers. This extension is obtained by quantifying atomic propositions, we call the resulting logic quanti ed mu-calculus. We study its main theoretical properties and show its adequacy to control applications. The proposed framework is expressive : it o ers a uniform way to describe as varied para...

We considered the problem of processing queries that contain generalized quanti ers. We demonstrate that current relational systems are ill-equipped, both at the language and at the query processing level, to deal with such queries. We propose a boolean matrix approach which establishes the feasibility of building systems that can process queries with generalized quanti ers e ciently, and we pr...

This paper discusses extensions to the language Ei el, required to write more comprehensive software speci cations, where a speci cation in Ei el is a collection of class interfaces with features speci ed using an assertion language (i.e. a BON static model). The focus of the paper is the extension of the assertion language with quanti cation. Two forms of quanti cation are identi ed, which are...

The paper consists of two parts. The rst one is a concise introduction to epistemic (both propositional and predicate) logic with common knowledge operator. As the full predicate logics of common knowledge are not even recursively enumerable, in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic operators to formulas with...

The monadic second-order quantiier alternation hierarchy over the class of nite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely nite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the diierence between the levels k +1 and k of the monadic hierarch...

We compare time needed for understanding di erent types of quanti ers. In the rst study, we show that the distinction between quanti ers recognized by nite-automata and push-down automata is psychologically relevant. In the second study, we compare comprehension of push-down quanti ers in universes with randomly placed objects and those where objects were ordered in some speci c way simplifying...