This article presents a computable criterion for the existence of a common invariant subspace of n×n complex matrices A1, . . . , As of a fixed dimension 1 ≤ d ≤ n. The approach taken in the paper is model-theoretic. Namely, the criterion is based on a constructive proof of the renowned Tarski’s theorem on quantifier elimination in the theory ACF of algebraically closed fields. This means that ...

Time is an important aspect of information in medical domains. In this paper, we adopt Allen's innuential interval algebra framework for representing temporal information. The interval algebra allows the representation of indeenite and incomplete information which is necessary in many applications. However, answering interesting queries in this framework has been shown to be almost assuredly in...

A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula. Satisfiability of this formula implies...

We present a rst-order modal-calculus which uses parameterised maximal x-points to describe safety and liveness properties of processes. Then we give a local model checking proof system for deciding if a process satisses such a formula. The processes we consider are those deenable in regular value-passing CCS with parameterised recursive deenitions. Certain rules in the proof system carry side ...

Recognizing mathematical expression is important to reduce time in converting image-based documents like PDF to text-based documents that are easy to use and edit. In case of general character recognition, the sequence of character segmentation is from left to right, and from top to bottom. However, mathematical expression is a kind of twodimension visual language. Thus, segmentation is more co...

Many temporal and modal logic languages can be regarded as subsets of rst order logic i e the semantics of a temporal logic formula is given as a rst order condition on points of the underlying models Kripke structures Often the set of possible models is restricted to models which are trees A temporal logic language is rst order expressively complete if for every rst order condition for a node ...

The interactive use of mathematical assistance systems requires an intensive training in their input and command language. With the integration into scientific WYSIWYG text-editors the author can directly use the natural language and formula notation she is used to. In the new documentcentric paradigm changes to the document are transformed by a mediator into commands for the mathematical assis...

1. revised and extended axiomatic theory and proof development. 2. a new curriculum with extensive questions, intuitive illustrations of key concepts, exercises in formal proofs, and an emphasis on the use of mathematical logic as a formal tool for the analysis of informal concept". 3. parallel languages-a completely new formal language containing concise formulas for use in proofs together wit...

Temporally extended goals are used in planning to express safety and maintenance conditions. Linear temporal logic is the language often used to express temporally extended goals. We present a method for compiling LTL goal formulas into Planning Domain Definition Language (PDDL), which is handled by many AI planners. The compilation process first constructs a finite state machine representing a...

1 The Arithmetic Hierarchy Our language or signature is 〈+, ·, <, 0, ′〉, denoted LPA. PA− is the theory of the positive part of discretely ordered rings in this language, consisting of e.g. the commutative, associate and distributive laws, the recursion equations for addition and multiplication, and ordering axioms. (See [2] page 16 for the exact definition of PA−.) The arithmetic hierarchy is ...