ŁΠ logic with fixed points

Łukasiewicz mu-Calculus

“…On the positive side, one can adapt the result of Proposition 2.3, using an embedding into the first order theory of real-closed fields, to prove that, although irrational, the values of Lukasiewicz terms extended with (co)multiplications are always algebraic. In a related direction, a fixed-point logic combining Lukasiewicz and (co)multiplication connectives, but based on the Brouwer fixed-point theorem (see discussion in Section 2), is investigated by Spada in [33].…”

Advances in the theory of L algebras

“…Let A be an LΠ 1 2 algebra, let F be the ordered field associated to it as in [19]. By Artin-Schreier Theorem F has an extension to a real closed field R. Clearly A embeds in the interval algebra of R, which is a µ LΠ algebra (for more details on the correspondence between µ LΠ algebras and real closed fields see [23]). Suppose now that there exist two, non-isomorphic, µ LΠ algebras B 1 and B 2 in which A embeds.…”

“…Recently an expansion of LΠ 1 2 logic with fixed points has been considered [23]. In the present work we study the algebraic semantics of this logic, namely µ LΠ algebras, from algebraic, model theoretic and computational standpoints.…”

“…Such algebraic structures were first introduced in [23], where their strict connection with real closed fields is shown. By exploiting this connection, we will give several algebraic, model-theoretic, and computational results.…”

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AbstractRecently an expansion of LΠ 1 2 logic with fixed points has been considered [23]. In the present work we study the algebraic semantics of this logic, namely µ LΠ algebras, from algebraic, model theoretic and computational standpoints.

We provide a characterisation of free µ LΠ algebras as a family of particular functions from [0, 1] n to [0,1].

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