This paper shows (1) the undecidability of the type checking and the typability problems in the domain-free lambda calculus with negation, product, and existential types, (2) the undecidability of the typability problem in the domain-free polymorphic lambda calculus, and (3) the undecidability of the type checking and the typability problems in the domain-free lambda calculus with function and ...

We suggest a new formalization of the existential termination problem of logic programs under the PROLOG leftmost selection rule and depth-rst computation rule. First of all, we give a characterization of the problem in terms of occurrence sets, by proving that a hprogram; goali existentially terminates if and only if there exists a nite correct occurrence set. Then we show that in order to stu...

We study the following natural variation on the classical universality problem: given an automaton M of some type (DFA/NFA/PDA), does there exist an integer l ≥ 0 such that Σl ⊆ L(M)? The case of an NFA was an open problem since 2009. Here, using a novel and deep construction, we prove that the problem is NEXPTIME-complete, and the smallest such l can be doubly exponential in the number of stat...

Universal/existential quantifiers can be seen as generalization of logical conjunction/disjunction. The universal (existential) quantification of an open proposition is the conjunction (disjunction) of all its possible instantiations. In other words, conjunction (disjunction) is a special kind of universal (existential) quantification where the domain of the variable is restricted to the set of...

A structure M is pregeometric if the algebraic closure is a pregeometry in all M ′ elementarily equivalent to M . We define a generalisation: structures with an existential matroid. The main examples are superstable groups of U-rank a power of ω and d-minimal expansion of fields. Ultraproducts of pregeometric structures expanding a field, while not pregeometric in general, do have an unique exi...

Background and Objectives: Infertility, particularly female infertility, can threat women's psychological health. Spiritual health can play a significant role in increasing people's abilities especially in tough conditions. The aim of this study was to investigate the effect of psychotherapy on existential health in infertile women. Methods: The study population of this experimental controlled...

Background: Nurses' direct exposure to COVID-19 patients and resulting health anxiety can threaten their performance of human and moral duties. Materials and Methods: This work was a descriptive correlational study. The statistical population was all nurses working in the intensive care unit of COVID-19 patients in Ardabil hospitals in the 2021 year, from which 150 people were selected by con...

We investigate the size of conjunctive query rewritings over OWL2QL ontologies of depth 1 and 2 by means of a new formalism, called hypergraph programs, for computing Boolean functions. Both positive and negative results are obtained. All conjunctive queries over ontologies of depth 1 have polynomial-size nonrecursive datalog rewritings; tree-shaped queries have polynomial-size positive existen...

We use the ϵ-determinant introduced by Ya-Jia Tan to define a family of ranks of matrices over certain semirings. We show that these ranks generalize some known rank functions over semirings such as the determinantal rank. We also show that this family of ranks satisfies the rank-sum and Sylvester inequalities. We classify all bijective linear maps which preserve these ranks.