Models and Games by Jouko Väänänen is a book that examines logic from a gametheoretic perspective. Games are nowadays considered to be a standard tool in mathematical logic. They are easy to describe and use and for this reason they have gained wide acceptance in logic during the second half of the twentieth century. Proofs involving games are easier to state and understand and may lead to nove...

Sketches as a method of specification of mathematical structures are an alternative to the string-based specification employed in mathematical logic. Sketch theory has been criticized as being lacunary when contrasted with logic because it apparently has nothing corresponding to proof theory. This article describes an approach to associating a proof-theoretic structure with a sketch. It is writ...

The eplex library of the ECLPS Constraint Logic Programming platform allows the integration of Mathematical Programming techniques with its native Constraint Logic Programming techniques within the same unified framework. It provides an interface to state-of-the-art Mathematical Programming solvers, and a set of programming primitives that allow ‘hybrid’ techniques to be easily expressed. This ...

There are two directions in my current research; I work in Set Theory and in interactions between Combinatorics and Logic. My research in set theory concerns the study of inner models of the set theoretic universe under assumptions of two kinds: (1) Forcing axioms, holding either in the universe V of all sets or in both V and the inner model under study, and (2) Agreement between (some of) the ...

An axiomatic theory represents mathematical knowledge declaratively as a set of axioms. An algorithmic theory represents mathematical knowledge procedurally as a set of algorithms. A biform theory is simultaneously an axiomatic theory and an algorithmic theory. It represents mathematical knowledge both declaratively and procedurally. Since the algorithms of algorithmic theories manipulate the s...

This paper presents a mathematical model for a flow shop scheduling problem consisting of m machine and n jobs with fuzzy processing times that can be estimated as independent stochastic or fuzzy numbers. In the traditional flow shop scheduling problem, the typical objective is to minimize the makespan). However,, two significant criteria for each schedule in stochastic models are: expectable m...

Traditionally the systematic study of animal behaviour using simulations requires the construction of a suitable mathematical model. The construction of such models in most cases requires advanced mathematical skills and exact knowledge of the studied animal's behaviour. Exact knowledge is rarely available. Usually it is available in the form of the observer's linguistic explanations and descri...

We extend the language of here-and-there logic by two kinds of atomic programs allowing to minimally update the truth value of a propositional variable here or there, if possible. These atomic programs are combined by the usual dynamic logic program connectives. We investigate the mathematical properties of the resulting extension of equilibrium logic: we prove that the problem of logical conse...