Menger systems of idempotent cyclic and weak near-unanimity multiplace functions

Multiplace functions, which are also called functions of many variables, and their algebras called Menger algebras have been studied in various fields of mathematics. Based on the theory of many-sorted algebras, the primary aim of this paper is to present the ideas of Menger systems and Menger systems of full multiplace functions which are natural generalizations of Menger algebras and Menger algebras of [Formula: see text]-ary operations, respectively. Two specific types of [Formula: see text]-ary operations, which are called idempotent cyclic and weak near-unanimity generated by cyclic and weak near-unanimity terms, are provided. The Menger algebras under consideration have a two-element universe, the elements of which are two specific [Formula: see text]-ary operations. Additionally, we provide necessary and sufficient conditions in which the abstract Menger algebra and the Menger algebras of these two [Formula: see text]-ary operations are isomorphic. An abstract characterization of unitary Menger systems via systems of idempotent cyclic and weak near-unanimity multiplace functions is generally investigated. A strong connection between clone of terms and Menger systems of full multiplace functions is also investigated.

Gibt es so etwas wie intellektuelle Toleranz?

In this article, it will be argued that tolerance is not necessarily a political or ethical, but rather an abstract attitude that can be applied to many different dimensions of normative evaluation. More specifically, it will be argued that there are genuinely intellectual forms of tolerance that are epistemically motivated and that need to be assessed on purely epistemic grounds. To establish this claim, an abstract characterization of tolerance will be applied to the epistemic phenomenon of disagreement in order to develop a specific conception of tolerance that picks out a genuinely intellectual attitude towards recognized disagreement. Since the attitude that is picked out by this conception is very popular and widespread, an epistemology of tolerance would be of great significance to our intellectual practice.

The Force of Assumptions and Self-Attributions

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A Syntactic Operator for Forgetting that Satisfies Strong Persistence

Whereas the operation of forgetting has recently seen a considerable amount of attention in the context of Answer Set Programming (ASP), most of it has focused on theoretical aspects, leaving the practical issues largely untouched. Recent studies include results about what sets of properties operators should satisfy, as well as the abstract characterization of several operators and their theoretical limits. However, no concrete operators have been investigated.In this paper, we address this issue by presenting the first concrete operator that satisfies strong persistence – a property that seems to best capture the essence of forgetting in the context of ASP – whenever this is possible, and many other important properties. The operator is syntactic, limiting the computation of the forgetting result to manipulating the rules in which the atoms to be forgotten occur, naturally yielding a forgetting result that is close to the original program.

Unifying Equivalences for Timed Transition Systems

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