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The relationship between MV-algebras and semirings was described by A. Di Nola and B. Gerla ([7]). Since commutative basic algebras are similar to MV-algebras up to associativity of the binary operation we try to get a similar relationship between commutative basic algebras and so-called near semirings and we show that this is possible. This means that… (More)

Main results of Dorninger and Länger (J Pure Appl Math 40:441–449, 2007) concerning polynomial permutations on bounded lattices with an antitone involu-tion are generalized to the case of bounded commutative directoids. Polynomial involutions are important in cryptography. Namely, if A ¼ ðA; FÞ is an algebra having a binary term operation ? such that the… (More)

The probability p(s) of the occurrence of an event pertaining to a physical system which is observed in different states s determines a function p from the set S of states of the system to [0, 1]. The function p is called a numerical event or multidimensional probability. When appropriately structured, sets P of numerical events form so-called algebras of… (More)

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