In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense ...

We introduce a new abstract domain, namely the domain of Interval Linear Equalities (itvLinEqs), which generalizes the affine equality domain with interval coefficients by leveraging results from interval linear algebra. The representation of itvLinEqs is based on a row echelon system of interval linear equalities, which natively allows expressing classical linear relations as well as certain t...

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...

We present a variant of the linear logical framework LLF that avoids the restriction that well-typed forms be in pre-canonical form and adds λ-abstraction at the level of families. We abandon the use of β-conversion as definitional equality in favor of a set of typed definitional equality judgments that include rules for parallel conversion and extensionality. We show type-checking is decidable...

Generalized Linear Models (GLZ) are an extension of the linear modeling process that allows models to be fit to data that follow probability distributions other than the Normal distribution, such as the Poisson, Binomial, Multinomial, and etc. Generalized Linear Models also relax the requirement of equality or constancy of variances that is required for hypothesis tests in traditional linear mo...

Instructor: Dieter van Melkebeek This lecture covers the notion of a linear program, its dual, and the relationship between the two. We give some examples and survey known algorithms. A linear program (LP) is the problem of optimizing (maximizing or minimizing) a linear multivariate objective function over the reals under linear equality and inequality (≤) constraints.

In ontology-based data access, data are queried through an ontology that offers a representation of the domain of interest. In this context, correct answers are those entailed by the logical theory constituted by the data and the ontology. Traditional database constraints like tuple-generating dependencies (TGDs) and equality-generating dependencies (EGDs) are a useful tool for ontology specifi...

Satisfiability Modulo Theories (SMT) solvers check the satisfiability of firstorder formulas written in a language containing interpreted predicates and functions. These interpreted symbols are defined either by first-order axioms (e.g. the axioms of equality, or array axioms for operators read and write,. . . ) or by a structure (e.g. the integer numbers equipped with constants, addition, equa...