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We extend the treatment of functional dependence, the basic concept of dependence logic, to include the possibility of dependence with a limited number of exceptions. We call this approximate dependence. The main result of the paper is a…
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
Building complex software systems necessitates the use of component-based architectures. In theory, of the set of components needed for a design, only some small portion of them are "custom"; the rest are reused or refactored existing…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
We consider systems whose lifetime is measured by the time of physical degradation of components, as well as the degree of power each component contributes to the system. The lifetimes of the components of the system are random variables.…
Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…
Many kinds of categorical structure require the existence of finite limits, of colimits of some specified type, and of "exactness" conditions between the finite limits and the specified colimits. Some examples are the notions of regular, or…
DefElement is an online encyclopedia of finite element definitions that was created and is maintained by the authors of this paper. DefElement aims to make information about elements defined in the literature easily available in a standard…
In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…
We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…
We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…
A number of exciting advances have been made in automated fact-checking thanks to increasingly larger datasets and more powerful systems, leading to improvements in the complexity of claims which can be accurately fact-checked. However,…
Background: Understanding the distinction between function and role is vexing and difficult. While it appears to be useful, in practice this distinction is hard to apply, particularly within biology. Results: I take an evolutionary…
A necessary and sufficient condition is given for a subshift presentation to have a continuous $g$-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous…
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…
Let $A$ be a set of natural numbers. A set $B$, a set of natural numbers, is said to be an additive complement of the set $A$ if all sufficiently large natural numbers can be represented in the form $x+y$, where $x\in A$ and $y\in B$. This…
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism…