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Proponiamo in questa Nota un quadro assiomatico aperto e non riduzionista, che si basa sulle idee primitive di qualità e relazione, in cui speriamo sia possibile innestare i concetti fondamentali della Matematica, della Logica e dell’Informatica (di cui diamo solo alcuni primissimi esempi). Auspichiamo che sviluppando liberamente tale quadro sia possibile giungere ad un fruttuoso confronto critico delle idee fondamentali delle diverse discipline scientifiche ed umanistiche, non ristretto agli «specialisti...
The elementary theory of ⟨α;×⟩, where α is an ordinal and × denotes ordinal multiplication, is decidable if and only if . Moreover if and respectively denote the right- and left-hand divisibility relation, we show that Th and Th are decidable for every ordinal ξ. Further related definability results are also presented.
In this paper we prove the decidability of the HD0L ultimate periodicity problem.
Various static analyses of functional programming languages
that permit infinite data structures make use of set
constants like Top, Inf, and Bot, denoting
all terms, all lists not eventually ending in Nil, and
all non-terminating programs, respectively. We use a set
language that permits union, constructors and recursive
definition of set constants with a greatest fixpoint semantics
in the set of all, also infinite, computable trees,
where all term constructors are non-strict.
This...
We consider logics on
and which are weaker than
Presburger arithmetic and
we settle the following decision
problem: given a k-ary
relation on and
which are first order definable in
Presburger arithmetic, are they definable in these
weaker logics? These logics, intuitively,
are obtained by considering modulo and threshold counting predicates for differences of two variables.
We consider the four families of recognizable, synchronous,
deterministic rational and rational subsets of a direct product
of free monoids.
They form a strict hierarchy and we investigate the following
decision problem: given a relation in one of the families,
does it belong to a smaller family?
We settle the problem entirely when all monoids have a unique
generator and fill some gaps in the general case.
In particular, adapting a proof of Stearns, we show that it is recursively decidable
whether...
In this paper we argue that for fuzzy unification we need a procedural and declarative semantics (as opposed to the two valued case, where declarative semantics is hidden in the requirement that unified terms are syntactically – letter by letter – identical). We present an extension of the syntactic model of unification to allow near matches, defined using a similarity relation. We work in Hájek’s fuzzy logic in narrow sense. We base our semantics on a formal model of fuzzy logic programming extended...
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