Related papers: Second-Order Algebraic Theories
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
This thesis deals with the specification and construction of syntax and operational semantics of a programming language. We work with a general notion of signature for specifying objects of a given category as initial objects in a suitable…
We investigate the extension of Monadic Second Order logic, interpreted over infinite words and trees, with generalized "for almost all" quantifiers interpreted using the notions of Baire category and Lebesgue measure.
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
This is the second of a series of articles providing a foundation for the theory of Drinfeld modular forms of arbitrary rank. In the present part, we compare the analytic theory with the algebraic one that was begun in a paper of the third…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
We present generalized algebraic theories corresponding to slightly modified versions of two of the type theories in our paper Type Theory with Explicit Universe Polymorphism. We first present a generalized algebraic theory for categories…
In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…
An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch can be any…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
This paper studies algebras arising as algebraic semantics for logics used to model reasoning with incomplete or inconsistent information. In particular we study, in a uniform way, varieties of bilattices equipped with additional…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…