7,607 research outputs found
A note on many valued quantum computational logics
The standard theory of quantum computation relies on the idea that the basic
information quantity is represented by a superposition of elements of the
canonical basis and the notion of probability naturally follows from the Born
rule. In this work we consider three valued quantum computational logics. More
specifically, we will focus on the Hilbert space C^3, we discuss extensions of
several gates to this space and, using the notion of effect probability, we
provide a characterization of its states.Comment: Pages 15, Soft Computing, 201
A Paraconsistent Higher Order Logic
Classical logic predicts that everything (thus nothing useful at all) follows
from inconsistency. A paraconsistent logic is a logic where an inconsistency
does not lead to such an explosion, and since in practice consistency is
difficult to achieve there are many potential applications of paraconsistent
logics in knowledge-based systems, logical semantics of natural language, etc.
Higher order logics have the advantages of being expressive and with several
automated theorem provers available. Also the type system can be helpful. We
present a concise description of a paraconsistent higher order logic with
countable infinite indeterminacy, where each basic formula can get its own
indeterminate truth value (or as we prefer: truth code). The meaning of the
logical operators is new and rather different from traditional many-valued
logics as well as from logics based on bilattices. The adequacy of the logic is
examined by a case study in the domain of medicine. Thus we try to build a
bridge between the HOL and MVL communities. A sequent calculus is proposed
based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker,
Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte
Conditionals and modularity in general logics
In this work in progress, we discuss independence and interpolation and
related topics for classical, modal, and non-monotonic logics
A one-valued logic for non-one-sidedness
Does it make sense to employ modern logical tools for ancient philosophy? This well-known debate2 has been re-launched by the indologist Piotr Balcerowicz, questioning those who want to look at the Eastern school of Jainism with Western glasses. While plainly acknowledging the legitimacy of Balcerowicz's mistrust, the present paper wants to propose a formal reconstruction of one of the well-known parts of the Jaina philosophy, namely: the saptabhangi, i.e. the theory of sevenfold predication. Before arguing for this formalist approach to philosophy, let us return to the reasons to be reluctant at it
Interval-valued algebras and fuzzy logics
In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter
Stone-type representations and dualities for varieties of bisemilattices
In this article we will focus our attention on the variety of distributive
bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and
involutive bisemilattices. After extending Balbes' representation theorem to
bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas-Dunn
duality and introduce the categories of 2spaces and 2spaces. The
categories of 2spaces and 2spaces will play with respect to the
categories of distributive bisemilattices and De Morgan bisemilattices,
respectively, a role analogous to the category of Stone spaces with respect to
the category of Boolean algebras. Actually, the aim of this work is to show
that these categories are, in fact, dually equivalent
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