A new formalization of Newman algebra.

A new branch of the logical algebra: UP-algebras

In this paper, we introduce a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms in UP-algebras, and investigated some related properties of them. We also describe connections between UP-ideals, UP-subalgebras, congruences and UP-homomorphisms, and show that the notion of UP-algebras is a ...

A Formalization of Unique Solutions of Equations in Process Algebra

In this thesis, a comprehensive formalization of Milner’s Calculus of Communicating Systems (also known as CCS) has been done in HOL theorem prover (HOL4), based on an old work in HOL88. This includes all classical properties of strong/weak bisimulation equivalences and observation congruence, a theory of congruence for CCS, various versions of “bisimulation up to” techniques, and several deep ...

A Formalization of the Process Algebra CCS in HOL4

An old formalization of the Process Algebra CCS (no value passing, with explicit relabeling operator) has been ported from HOL88 theorem prover to HOL4 (Kananaskis-11 and later). Transitions between CCS processes are defined by SOS (Structural Operational Semantics) rules, then algebaric laws for strong equivalence (including the expansion law) were proved upon SOS transition rules. We used HOL...

A New Formalization of Probabilistic GLR Parsing

This paper presents a new formalization of probabilistic GLR language modeling for statistical parsing. Our model inherits its essential features from Briscoe and Carroll's generalized probabilistic LR model [3], which obtains context-sensitivity by assigning a probability to each LR parsing action according to its left and right context. Briscoe and Carroll's model, however, has a drawback in ...

Formalization and Execution of Linear Algebra: From Theorems to Algorithms