In this paper, the notions of $(T,S)$-composition matrix and$(T,S)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(T,S)$ is a dual pair of triangular module. Theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. Furthermore, theirproperties and characterizations are presented. Then a new methodbased on $tilde{...

Framing effects are said to occur when equivalent frames lead to different choices. However, the equivalence in question has been incompletely conceptualized. In a new normative analysis of framing effects, we complete the conceptualization by introducing the notion of information equivalence. Information equivalence obtains when no choice-relevant inferences can be drawn from the speaker s cho...

We present a complete reasoning principle for contextual equivalence in an untyped probabilistic programming language. The language includes continuous random variables, conditionals, and scoring. The language also includes recursion, since in an untyped language the standard call-by-value fixpoint combinator is expressible. The language is similar to that of Borgström et al. [5]. To demonstrat...

We develop an operational theory of higher-order functions, recursion, and fair non-determinism for a non-trivial, higher-order, call-by-name functional programming language extended with McCarthy's amb. Implemented via fair parallel evaluation, functional programming with amb is very expressive. However, conventional semantic xed point principles for reasoning about recursion fail in the prese...

We apply Andy Pitts’s methods of defining relations over domains to several classical results in the literature. We show that the Y combinator coincides with the domaintheoretic fixpoint operator, that parallel-or and the Plotkin existential are not definable in PCF, that the continuation semantics for PCF coincides with the direct semantics, and that our domain-theoretic semantics for PCF is a...

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

This dissertation contributes to analysis methods for infinite-state systems. The dissertation focuses on equivalence testing for two relevant classes of infinite-state systems: commutative context-free processes, and one-counter automata. As for equivalence notions, we investigate the classical bisimulation and simulation equivalences. The important point is that we allow for silent steps in t...

In general, disjunction is considered to add expressive power to propositional logic programs under stable model semantics, and to enlarge the range of problems which can be expressed. However, from a semantical point of view, disjunction is often not really needed, in that an equivalent program without disjunction can be given. We thus consider the question, given a disjunctive logic program ,...

For an operator T in the class Bn(Ω), introduced in [4], the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle ET determine the unitary equivalence class of the operator T . In the paper [6], the authors ask if there exists some pair of inequivalent oprators T1 and T2 for which the simultaneous unitary equival...

A typical software module evolves through many versions over the course of its development. To maintain compatibility with module clients, it is crucial that a module’s behavior at its interface does not change in an undesirable manner across versions. The problem of introducing changes which break interface behavior remains one of the most daunting challenges in the maintenance of large softwa...