Appendix: Conjectures Concerning Proof, Design, and Verification

This article focuses on an esoteric but practical use of automated reasoning that may indeed be new to many, especially those concerned primarily with verification of both hardware and software. Specifically, featured are a discussion and some methodology for taking an existing design -- of a circuit, a chip, a program, or the like--and refining and improving it in various ways. Although the methodology is general and does not require the use of a specific program, McCune's program OTTER does offer what is needed. OTTER has played and continues to play the key role in my research, and an interested person can gain access to this program in various ways, not the least of which is through the included CD-ROM in [3]. When success occurs, the result is a new design that may require fewer components, avoid the use of certain costly components, offer more reliability and ease of verification, and, perhaps most important, be more efficient in the contexts of speed and heat generation. Although the author has minimal experience in circuit design, circuit validation, program synthesis, program verification, and similar concerns, (at the encouragement of colleagues based on successes to be cited) he presents materials that might indeed be of substantial interest to manufacturers and programmers. He writes this article in part prompted by the recent activities of chip designers that include Intel and AMD, activities heavily emphasizing the proving of theorems. As for his research that appears to the author to be relevant, he has made an intense and most profitable study of finding proofs that are shorter [2,3], some that avoid the use of various types of term, some that are far less complex than previously known, and the like. Those results suggest to me a strong possible connection between more appealing proofs (in mathematics and in logic) and enhanced and improved design of both hardware and software. Here the author explores diverse conjectures that elucidate some of the possibly fruitful connections

Automating Emendations of the Ontological Argument in Intensional Higher-Order Modal Logic

A shallow semantic embedding of an intensional higher-order modal logic (IHOML) in Isabelle/HOL is presented. IHOML draws on Montague/Gallin intensional logics and has been introduced by Melvin Fitting in his textbook Types, Tableaus and Gödel’s God in order to discuss his emendation of Gödel’s ontological argument for the existence of God. Utilizing IHOML, the most interesting parts of Fitting’s textbook are formalized, automated and verified in the Isabelle/HOL proof assistant. A particular focus thereby is on three variants of the ontological argument which avoid the modal collapse, which is a strongly criticized side-effect in Gödel’s resp. Scott’s original work

Listening to the voices of women suffering perinatal psychological distress

This article suggests that transactional analysis can be an effective treatment approach for women suffering from mental health conditions and the emotional and life disturbances that may occur during the perinatal period. It offers a brief introduction to perinatal psychological distress followed by a description of the use of transactional analysis psychotherapy for this condition. The article outlines a new model for a research project that aims to ascertain women’s views on the helpfulness of the treatment and to gain a better understanding of the stigma often associated with perinatal mental health issues. The author argues for the necessity of qualitative research to assess the efficacy of transactional-analysis-based treatment and to increase our knowledge about the change process in transactional analysis psychotherapy with this client population as well as to inform future transactional analysis treatment protocols