Motivated by the model theory of higher order logics, in [2] a certain kind of topological spaces had been introduced on ultraproducts. These spaces are called ultratopologies. Ultratopologies provide a natural extra topological structure for ultraproducts and using this extra structure in [2] some preservation and characterization theorems had been obtained for higher order logics. The purely ...

Alfred Tarski’s influence on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is Tarski’s work on the decision procedure for algebra and geometry, the method of elimination of quantifiers, the semantics of formal languages, model-theoretic preservation theorems, and algebraic logic; various connections of each with co...

The paper studies basic graded properties of unary and binary fuzzy connectives, i.e., unary and binary operations on the set of truth degrees of a background fuzzy logic extending the logic MTL of left-continuous t-norms. The properties studied in this paper are graded generalizations of monotony, Lipschitz continuity, null and unit elements, idempotence, commutativity, and associativity. The ...

The groupoid interpretation of Martin-Löf type theory not only shows the independence of uniqueness of identity proofs from the axioms of intensional type theory but is also constructive and validates the computation rules as definitional equalities. The groupoid semantics are very clear when interpreting dependent types and in particular the identity types but less so when defining equality pr...

FC, the core language of the Glasgow Haskell Compiler, is an explicitly-typed variant of System F with first-class type equality proofs (i.e. coercions). This extensible proof system forms the foundation for type system extensions such as type families (typelevel functions) and Generalized Algebraic Datatypes (GADTs). Such features, especially in conjunction with kind polymorphism and datatype ...

In digitizing 3D objects one wants as much as possible object properties to be preserved in its digital reconstruction. One of the most fundamental properties is topology. Only recently a sampling theorem for cubic grids could be proved which guarantees topology preservation [1]. The drawback of this theorem is that it requires more complicated reconstruction methods than the direct representat...

program schemes, such as scan or homomorphism, can capture a wide range of data parallel programs. While versatile, these schemes are of limited practical use on their own. A key problem is that the more natural sequential spec-iications may not have associative combine operators required by these schemes. As a result, they often fail to be immediately identiied. To resolve this problem, we pro...

We present a generic framework to transform a single-threaded operational semantics into a semantics with interleaved execution of threads. Threads can be dynamically created and use locks for synchronisation. They can suspend themselves, be notified by other threads again, and interact via shared memory. We formalised this in the proof assistant Isabelle/HOL along with theorems to carry type s...

In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...