This paper provides formal semantics for an extension of the ObjectRole Modeling approach that supports declaration of dynamic rules. Dynamic rules differ from static rules by pertaining to properties of state transitions, rather than to the states themselves. In this paper we restrict application of dynamic rules to so-called single-step transactions, with an old state (the input of the transa...

Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as of the λ-binder of the lambda-calculus or the ∀binder of first-order logic. It also allows us to finitely axiomatise arithmetic, and similarly to axiomatise ‘nominal’ datatypes-with-binding. Just like ...

We propose a language which can express every computable query. The language is syntactically based on the first-order predicate calculus, but semantically is interpreted as post-conditions, unlike the customary calculus query languages. The language has a capability to restrict itself to reasonable queries, accepting criteria of reasonability as a parameter.

Let / be any fixed positive integer and a a sentence in the first-order predicate calculus of/unary functions. For positive integers n, an «-structure is a model with universe {0,1,...,« 1} and/unary functions, and p(n,a) is the ratio of the number of «-structures satisfying a to n"f, the number of «-structures. We show that lim„_00/i(«, a) exists for all such a, and its value is given by an ex...

We investigate a construction schema for first-order logical systems, called “form logic”. Form logic allows us to overcome the dualistic commitment of predicate logic to individual constants and predicates. Dualism is replaced by a pluralism of terms of different “logical forms”. Individual form-logical systems are generated by the determination of a range of logical forms and of the formbased...

Model reduction and convex optimization are prevalent in science and engineering applications. In this thesis, convex optimization solution techniques to three different model reduction problems are studied. Parameterized reduced order modeling is important for rapid design and optimization of systems containing parameter dependent reducible sub-circuits such as interconnects and RF inductors. ...

We investigate the translocation of a single stranded DNA (ssDNA) through a pore, which fluctuates between two conformations, by using coupled master equations (ME). The probability density function (PDF) of the first passage times (FPT) of the translocation process is calculated, displaying a triple, double or mono-peaked behavior, depending on the system parameters. An analytical expression f...

K urt Gödel (1906–1978), with his work on the constructible universe L, established the relative consistency of the Axiom of Choice and the Continuum Hypothesis. More broadly, he secured the cumulative hierarchy view of the universe of sets and ensured the ascendancy of first-order logic as the framework for set theory. Gödel thereby transformed set theory and launched it with structured subjec...