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This paper gives a semantical underpinning for a many-sorted modal logic associated with certain dynamical systems, like transition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial functors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many-sorted Boolean Algebras with...
This paper gives a semantical underpinning for a many-sorted modal
logic associated with certain dynamical systems, like transition
systems, automata or classes in object-oriented languages. These
systems will be described as coalgebras of so-called polynomial
functors, built up from constants and identities, using products,
coproducts and powersets. The semantical account involves Boolean
algebras with operators indexed by polynomial functors, called MBAOs,
for Many-sorted Boolean Algebras with...
In a Boolean Algebra B, an inequality f(x,x --> y)) ≤ y satisfying the condition f(1,1)=1, is considered for defining operations a --> b among the elements of B. These operations are called Conditionals'' for f. In this paper, we obtain all the boolean Conditionals and Internal Conditionals, and some of their properties as, for example, monotonicity are briefly discussed.
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