Domain Representations Induced by Dyadic Subbases

We study domain representations induced by dyadic subbases and show that a proper dyadic subbase S of a second-countable regular space X induces an embedding of X in the set of minimal limit elements of a subdomain D of $\{0,1,\perp\}\omega$. In particular, if X is compact, then X is a retract of the set of limit elements of D

A Domain-theoretic Semantics of Lax Generic Functions

AbstractThe semantic structure of a calculus λm is studied. λm is a polymorphic calculus defined over a hierarchical type structure, and a function in this calculus, called a generic function, can be composed from more than one lambda expression and the ways it behaves on each type are weakly related in that it lax commutes with coercion functions.Since laxness is intermediate between ad-hocness and coherentness, λm has syntactic properties lying between those of calculi with ad-hoc generic functions and coherent generic functions studied in [Tsu95]. That is, though λm allows self application and thus is not normalizing, it does not have an unsolvable term. For this reason, all the semantic domains are connected by infinitely many mutually recursive equations and, at the same time, they do not have the least elements. We solve them by considering opfibrations and expressing the equations as one recursive equation about opfibrations. We also show the adequacy theorem for λm following the construction of A. Pitts and use it to derive some syntactic properties

Dyadic Subbases and Representations of Topological Spaces

We explain topological properties of the embedding-based approach to computability on topological spaces. With this approach, he considered a special kind of embedding of a topological space into Plotkin\u27s $T^omega$, which is the set of infinite sequences of $T = {0,1,bot }$. We show that such an embedding can also be characterized by a dyadic subbase, which is a countable subbase $S = (S_0^0, S_0^1, S_1^0, S_1^1, ldots)$ such that $S_n^j$ $(n = 0,1,2,ldots; j = 0,1$ are regular open and $S_n^0$ and $S_n^1$ are exteriors of each other. We survey properties of dyadic subbases which are related to efficiency properties of the representation corresponding to the embedding

A Study of Refusal Strategies by American and International Students at an American University

Refusals are delicate speech acts for non-native speakers to negotiate because they require negative responses to an interlocutor\u27s invitation or request. In addition to cultural variation, variables such as gender and modes of communication (e.g., emails) add dimensions to the complexity when performing refusals. The main objective of this study is to investigate the difference in refusal strategies between American and international college students as well as gender variation. Using a written Discourse Completion Task, six situations were developed and grouped in two stimulus types eliciting refusals to an invitation and a request. Each stimulus type involved an email refusal to professors, friends, and a staff member of an academic department. The refusals of sixteen undergraduate American students and thirty-two international students were analyzed in terms of frequency, order, and content of semantic formulas. The results of this study suggest that when using email, all groups demonstrated preference for direct refusal. American females preferred expressions of gratitude and stating positive opinions, whereas American male provided reasons and alternatives. The international students used a greater variety of semantic formulas; however, they lacked positive opinions and providing alternatives. Additionally, the international students tended to use more regret than the American students. The international students (both male and female) also tended to use more specific excuses as compared to more general excuses used by the Americans

Lawson topology of the space of formal balls and the hyperbolic topology

AbstractLet (X,d) be a metric space and BX=X×R denote the partially ordered set of (generalized) formal balls in X. We investigate the topological structures of BX, in particular the relations between the Lawson topology and the product topology. We show that the Lawson topology coincides with the product topology if (X,d) is a totally bounded metric space, and show examples of spaces for which the two topologies do not coincide in the spaces of their formal balls. Then, we introduce a hyperbolic topology, which is a topology defined on a metric space other than the metric topology. We show that the hyperbolic topology and the metric topology coincide on X if and only if the Lawson topology and the product topology coincide on BX

Extracting total Amb programs from proofs

We present a logical system CFP (Concurrent Fixed Point Logic) supporting the extraction of nondeterministic and concurrent programs that are provably total and correct. CFP is an intuitionistic first-order logic with inductive and coinductive definitions extended by two propositional operators: Rrestriction, a strengthening of implication, and an operator for total concurrency. The source of the extraction are formal CFP proofs, the target is a lambda calculus with constructors and recursion extended by a constructor Amb (for McCarthy's amb) which is interpreted operationally as globally angelic choice and is used to implement nondeterminism and concurrency. The correctness of extracted programs is proven via an intermediate domain-theoretic denotational semantics. We demonstrate the usefulness of our system by extracting a nondeterministic program that translates infinite Gray code into the signed digit representation. A noteworthy feature of CFP is the fact that the proof rules for restriction and concurrency involve variants of the classical law of excluded middle that would not be interpretable computationally without Amb.Comment: 39 pages + 4 pages appendix. arXiv admin note: text overlap with arXiv:2104.1466

A Stream Calculus of Bottomed Sequences for Real Number Computation

AbstractA calculus XPCF of 1⊥-sequences, which are infinite sequences of {0,1,⊥} with at most one copy of bottom, is proposed and investigated. It has applications in real number computation in that the unit interval I is topologically embedded in the set Σ⊥,1ω of 1⊥-sequences and a real function on I can be written as a program which inputs and outputs 1⊥-sequences. In XPCF, one defines a function on Σ⊥,1ω only by specifying its behaviors for the cases that the first digit is 0 and 1. Then, its value for a sequence starting with a bottom is calculated by taking the meet of the values for the sequences obtained by filling the bottom with 0 and 1. The validity of the reduction rule of this calculus is justified by the adequacy theorem to a domain-theoretic semantics. Some example programs including addition and multiplication are shown. Expressive powers of XPCF and related languages are also investigated

Missions of Small Satellites Launched by the J-I Launch Vehicle

This paper presents the concept of the small satellites launched by the 1-1 launch vehicle of the National Space Development Agency of JAPAN (NASDA). On this concept, the missions of the small satellites are for the experiment and the validation of the earth observation. The satellite communications, and the others on orbit. For efficient achievements of these missions, the common satellite bus will be adopted for the solid launch vehicle J-I, in order to develop the each small satellite system quickly by low-cost