These notes were prepared for the UC Berkeley Group in Logic & the Methodology of Science foundations exam. Material is adapted from Chang and Keisler’s (1973) Model Theory and Wilfrid Hodges’ (1997) A Shorter Model Theory. Sections 1-2 review basic semantic/syntactic concepts; Section 3 introduces Robinson diagrams and canonical interpretations; Section 4 presents backand-forth techniques; Sec...

This technical report presents a type soundness proof for Core CGen, a small, formal language designed for studying the addition of a component system based on genericity to a nominally typed objectoriented language supporting first-class generics. Core CGen captures the most intricate aspects of the Component NextGen programming language, an extension of the NextGen architecture that provides ...

Y. Ling, H. Cao,* A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang Department of Physics and Astronomy, Materials Research Center, Northwestern University, Evanston, Illinois 60208-3112 Department of Chemistry, Materials Research Center, Northwestern University, Evanston, Illinois 60208-3113 Department of Materials Science and Engineering, Materials Research Center, Northwestern University...

Introduction Body movements, including gestures, provide different learning channels for students, which may help them to more easily understand learning materials (Hostetter & Alibali, 2008; Tellier, 2008; Wilson, 2002). From this perspective, the purpose of using gestures is to help learners improve their comprehension and build connections between the materials and gestures. In addition to s...

There is a natural action of SL(2,R) on the moduli space of translation surfaces, and this yields an action of the unipotent subgroup U = {( 1 ∗ 0 1 )} . We classify the U -invariant ergodic measures on certain special submanifolds of the moduli space. (Each submanifold is the SL(2,R)-orbit of the set of branched covers of a fixed Veech surface.) For the U -action on these submanifolds, this is...

Semantic preservation by compilers for higher-order languages can be verified using simple syntactic methods. At the heart of classic techniques are relations between source-level and target-level values. Unfortunately, these relations are specific to particular compilers, leading to correctness theorems that have nothing to say about linking programs with functions compiled by other compilers ...

 Many Limit Theorems, Convergence Theorems and Characterization Theorems in Probability and Statistics, in particular those related to normal distribution , are based on the assumption of independence of two or more random variables. However, the full power of independence is not used in the proofs of these Theorems, since it is the distribution of summation of the random variables whic...

in this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.

Languages are constantly evolving through their users due to the need to communicate more efficiently. Under this hypothesis, we formulate unsupervised word segmentation as a regularized compression process. We reduce this process to an optimization problem, and propose a greedy inclusion solution. Preliminary test results on the Bernstein-Ratner corpus and Bakeoff-2005 show that the our method...