Zeroth order logic is a term in popular use among practitioners for the common principles underlying the algebra of sets, boolean algebra, boolean functions, logical connectives, monadic predicate calculus, propositional calculus, and sentential logic. The term serves to mark a level of abstraction in which the more inessential differences among these subjects can be subsumed under the appropriate isomorphisms.
Suppose that we wanted to construct a mathematical universe where all objects were computable in some sense. How would we do it? Well, we could certainly allow the set \mathbb{N} into our universe: natural numbers are the most basic computational objects there are. (Notation: I’ll use N to refer to \mathbb{N} when we’re considering it as part of the universe we’ll building, and just \mathbb{N} when we’re talking about the set of natural numbers in the “real” world.) What should we take as our set of functions N^N from N to N? Since we want to admit only computable things, we should let N^N be the set of computable functions from \mathbb{N} to \mathbb{N}, which we can represent non-uniquely by their indices (i.e., by the programs which compute them).
Information vs Knowledge To a machine, knowledge is comprehended information (aka new information produced through the application of deductive reasoning to exiting information). To a machine, information is only data, until it is processed and compr
Information vs Knowledge To a machine, knowledge is comprehended information (aka new information produced through the application of deductive reasoning to exiting information). To a machine, information is only data, until it is processed and compr
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