A family of Gödel hybrid logics

In this paper, we define a family of fuzzy hybrid logics that are based on Gödel logic. It is composed of two infinite-valued versions called ${\mathsf{GH}}_{\infty }$ and ${\mathsf{WGH}}_{\infty }$, and a sequence of finitary valued versions ${({\mathsf{GH}}_n)}_{0<n<\infty }$. We define decision procedures for both ${\mathsf{WGH}}_{\infty }$ and ${({\mathsf{GH}}_n)}_{0<n<\infty }$ that are based on particular sequents and on a set of proof rules dealing with such sequents. As these rules are strongly invertible the procedures naturally allow one to generate countermodels. Therefore we prove the decidability and the finite model property for these logics. Finally, from the decision procedure of ${\mathsf{WGH}}_{\infty }$, we design a sound and complete sequent calculus for this logic.     

The Power of Belnap: Sequent Systems for <Emphasis Type="BoldItalic">SIXTEEN</Emphasis><Subscript><Emphasis Type="Bold">3</Emphasis></Subscript>

The trilattice SIXTEEN₃\textit{SIXTEEN}_3 is a natural generalization of the well-known bilattice FOUR₂\textit{FOUR}_2. Cut-free, sound and complete sequent calculi for truth entailment and falsity entailment in SIXTEEN₃\textit{SIXTEEN}_3 are presented.     

Women with <Emphasis Type="Italic">BRCA1</Emphasis> or <Emphasis Type="Italic">BRCA2</Emphasis> Mutations Renegotiating a Post-Prophylactic Mastectomy Identity: Self-Image and Self-Disclosure.

The Facing Our Risk of Cancer Empowered (FORCE) website is devoted to women at risk for hereditary breast and ovarian cancers. One of the most frequently discussed topics on the archived messaged board has been prophylactic mastectomy (PM) for women with a BRCA1/2 mutation. We reviewed the messages, over a 4 year period, of 21 high risk women and their “conversational” partners who originally posted on a thread about genetic testing, genetic counseling and family history. We used a qualitative research inductive process involving close reading, coding and identification of recurrent patterns, relationships and processes in the data. The women sought emotional support, specific experiential knowledge and information from each other. They frequently found revealing their post PM status problematic because of possible negative reactions and adopted self-protective strategies of evasion and concealment outside of their web-based community. The FORCE message board was considered to be a safe place in which the women could be truthful about their choices and feelings. Results are discussed in terms of Goffman’s concepts “stigma” and “disclosure” and Charmaz’s concepts “interruptions,” “intrusions” and a “dreaded future.”     

Analytic Tableaux for all of <Emphasis Type="Italic">SIXTEEN</Emphasis><Subscript>3</Subscript>

In this paper we give an analytic tableau calculus P L _{1 6} for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ? _t , ? _f , ? _i , and ? under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment relations will in general require developing four tableaux, while proving that they are in the ? relation may require six.     

Three-Valued Temporal Logic <Emphasis Type="Italic">Q</Emphasis><Subscript><Emphasis Type="Italic">t</Emphasis></Subscript> and Future Contingents

Prior’s three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic Q _t and give its axiomatization and semantics. We also argue that Q _t provides a smooth solution to the problem of future contingents. Presented by Daniele Mundici     

On Some Much Maligned Remarks of Wittgenstein on Gödel

In Remarks on the Foundations of Mathematics Wittegnstein discusses an argument that goes from Gödel's incompleteness result to the conclusion that some truths of mathematics are unprovable. Wittegnstein takes issue with this argument. Wittegnstein's remarks in this connection have received very negative reaction from some very prominent people, for example, Gödel and Dummett. The paper is a defense of what Wittegnstein has to say about the argument in question.