Fredkin Gates for Finite-valued Reversible and Conservative Logics

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram

Games for the Strategic Influence of Expectations

We introduce a new class of games where each player's aim is to randomise her strategic choices in order to affect the other players' expectations aside from her own. The way each player intends to exert this influence is expressed through a Boolean combination of polynomial equalities and inequalities with rational coefficients. We offer a logical representation of these games as well as a computational study of the existence of equilibria.Comment: In Proceedings SR 2014, arXiv:1404.041

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets

Some Epistemic Extensions of G\"odel Fuzzy Logic

In this paper, we introduce some epistemic extensions of G\"odel fuzzy logic whose Kripke-based semantics have fuzzy values for both propositions and accessibility relations such that soundness and completeness hold. We adopt belief as our epistemic operator, then survey some fuzzy implications to justify our semantics for belief is appropriate. We give a fuzzy version of traditional muddy children problem and apply it to show that axioms of positive and negative introspections and Truth are not necessarily valid in our basic epistemic fuzzy models. In the sequel, we propose a derivation system $K_F$ as a fuzzy version of classical epistemic logic $K$. Next, we establish some other epistemic-fuzzy derivation systems $B_F, T_F, B_F^n$ and $T_F^n$ which are extensions of $K_F$, and prove that all of these derivation systems are sound and complete with respect to appropriate classes of Kripke-based models