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...

We present a road map for a joint project of the simulation league and the humanoid league that we call 3D2Real. This project is concerned with the integration of these two leagues which is becoming increasingly important as the research fields are converging. Currently, a lot of work is duplicated across the leagues, collaboration is sparse, and knowhow is not transfered effectively. This bind...

ion Let τ = λx.σ. By the induction hypothesis, σ defines a function of its free variables. Let those free variables be of types D0, . . . ,Dn where Dn is the type of x. Then σ defines an approximable function g : D0 × . . .×Dn → D′ where D′ is the type of σ. Using Theorem 3.12, the function curry(g) : D0 × . . .×Dn−1 → (Dn → D′) yields an approximable function, but this is just the function def...

The paper considers the set ML1 of rst-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using the mosaic technique, we prove a general satissability criterion for formulas in ML1 which reduces the modal satissability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragm...

Van Lambalgen (1991) proposed a translation from a language containing a generalized quanti er Q into a rst-order language enriched with a family of predicates R i , for every arity i (or an in nitary predicate R) which takes Qx (x; y 1 ; : : : ; y n ) to 8x(R(x; y 1 ; : : : ; y n ) ! (x;y 1 ; : : : ; y n )) (y 1 ; : : : ; y n are precisely the free variables of Qx ). The logic of Q (without or...

Second order uni cation is undecidable in general Miller showed that uni cation of so called higher order patterns is decidable and unitary We show that the uni cation of a linear higher order pat tern s with an arbitrary second order term that shares no variables with s is decidable and nitary A few extensions of this uni cation problem are still decidable unifying two second order terms where...

A new simple model is introduced for a liquid and an equation of state is derived based on this model and the statistical mechanical calculations. This equation of state works well for the non-polar and slightly polar liquids. The important conclusion that may be deduced from this equation of state is that if the reduced variables of state are chosen and defined appropriately, then, the pri...

This paper serves as a self-contained, tutorial introduction to combinatory models of the untyped lambda calculus. We focus particularly on the interpretation of free variables. We argue that free variables should not be interpreted as elements in a model, as is usually done, but as indeterminates. We claim that the resulting interpretation is more natural and leads to a closer correspondence b...

In [9] we introduced a new framework for asymptotic probabilities. in which a r i-add~t~ve measure is defined on the sample space of all sequences A =< dl.d?. . d, > of finite models. where the uniberse of sf,, is { I . 2. ...n ) . In this framework we Investigated the strong 0-1 law for sentences. whlch states that each sentence either holds in d,, eventually almost surely or fails In d,, even...