Background: The informal caregivers of the patients with COVID-19, who are in direct contact with patients and Coronavirus, experience many psychological issues and are prone to illness anxiety disorder. Therefore, this study was conducted with the aim of determining the effect of virtual training of Benson relaxation technique on illness anxiety disorder in the informal caregivers of the patie...

We show how solutions to typical problems of High School and rst-year University mathematics can be written using structured derivations. Such a derivation extends the calculational proof format with subderivations that allow inferences to presented at diierent levels of detail. By using structured derivations and a minimal amount of logical syntax, we can write solution to typical problems in ...

2 From Modal -Calculus to Alternating Tree Automata 4 2.1 Modal -Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Kripke Structures . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.3 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.4 Semantics . . . . . . . . . . . . . . . . . . . . . ....

The PCP Theorem is concerned with the notion of “proofs” for mathematical statements. We begin with a somewhat informal definition: Definition 1.1. A traditional proof system works as follows: • A statement is given. (e.g., “this graph G = · · · is 3-colorable” or “this CNF formula F = (x1 ∨ x2 ∨ x10) ∧ · · · is satisfiable”). • A prover writes down a proof, in some agreed-upon format. • A veri...

the informality of possession and lack of security in residence are among the characteristics attributed to the informal settlements, as well as, they are a key to other problems’ solutions. this essay investigates some of the typical cases of iran’s informal settlements, and this intends to find out the possession conditions, as well as, the conditions necessary for the recognition of the ...

Bundy and Richardson [7] presented a technique for reasoning about lists using ellipsis (the dots in 1+2+ . . .+10), where a polymorphic function, denoted by 2, is used to encapsulate recursive definitions of list functions and a portrayal system using ellipsis gives an informal proof. We highlight certain limitations of this technique and address these limitations using the recently developed ...

In [4] an informal algorithm ’to display interesting numeric patterns’ is described without any proof. We generalize this algorithm over arbitrary finite fields of characteristic p and we prove that it really generates self-similar carperts, provided that they contain at least one zero in the first (p+1)/2 lines. For the fields Fp the generalized algorithm produces p− 1 different self-similar c...

Despite the science of modern formal reasoning being more than a century old, mechanized formal reasoning is nowhere near what expert human reasoners (formal and informal) can achieve. Meanwhile, there is a steadily increasing need for automated theorem proving in various fields of science and engineering. Proof discovery and verification in science and mathematics [2,3,4,5], formal verificatio...

Thambidurai and Park 13] have proposed an algorithm for Interactive Consistency that retains resilience to the arbitrary (or Byzantine) fault mode, while tolerating more faults of simpler kinds than standard Byzantine-resilent algorithms. Unfortunately, and despite a published proof of correctness, their algorithm is awed. We detected this while undertaking a formal veriication of the algorithm...

We propose a dependently typed formalization for a simple class of sequential decision problems. For this class of problems, we implement a generic version of Bellman’s backwards induction algorithm [2] and a machine checkable proof that the proposed implementation is correct. The formalization is generic. It is presented in Idris, but it can be easily translated to other dependently-typed prog...