We give a purely syntactic proof (from scratch) of the subject equality property of the BCD intersection type system through a reformulation of the subtyping relation having a “cutelimination” property.

We prove an extensionality theorem for the “type-in-type” dependent type theory with Σ-types. We suggest that the extensional equality type be identified with the logical equivalence relation on the free term model of type theory.

Isomorphism is an equivalence relation that is less stringent than identity (equality), and it is useful for synthetic analysis, since it allows one to find reflexive routes for targets even when they do not have an element of symmetry.

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...

This paper introduces properties preset-equality for equalconflict Petri nets and enabling-equivalence for their reachability graphs. It explores the relation between these properties and shows its use for synthesis of equal-conflict Petri nets from labelled transition systems.

Recently several researchers have investigated-equality for the simply typed-calculus with exponentials, products and unit types. In these works,-conversion was interpreted as an expansion with syntactic restrictions imposed to prevent the expansion of introduction terms or terms which form the major premise of elimination rules. The resulting rewrite relation was shown connuent and strongly no...

26 the descriptive power of RMIN and the simplicity of its semantics, they provide a powerful incentive for further investigation of RMIN in combination with ACL as the basis of a formal software development method. Notes 1. In fact it is only when using a typed theory that there is a problem with undeened terms. In untyped axiomatic set theory the application of a function outside its domain c...

Roughly, we define a redundant relation in a database instance (dbi) as a k-ary relation R such that there is a first-order query which evaluated in the reduced dbi, gives us R. So, we can eliminate that relation R as long as the equivalence classes of the relation of equality of the first-order types for all k-tuples in the dbi are not altered. It turns out that in a fixed dbi, the problem of ...

One can add the machinery of relation symbols and terms to a propositional modal logic without adding quantifiers. Ordinarily this is no extension beyond the propositional. But if terms are allowed to be non-rigid, a scoping mechanism (usually written using lambda abstraction) must also be introduced to avoid ambiguity. Since quantifiers are not present, this is not really a first-order logic, ...

The Constraint Hierarchy (CH) framework is used to tackle multiple criteria selection (MCS), consisting of a set of candidates and a set of, possibly competing, criteria for selecting the \best" candidate(s). In this paper, we identify aspects of the CH framework for further enhancement so as to model and solve MCS problems more accurately. We propose the Fuzzy Constraint Hierarchies framework,...