Coherence in Modal Logic

A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform deductive interpolation property for equational consequence in a variety, and a general criterion was given for the failure of coherence (and hence uniform deductive interpolation) in varieties of algebras with a term-definable semilattice reduct. In this paper, a more general criterion is obtained and used to prove the failure of coherence and uniform deductive interpolation for a broad family of modal logics, including K, KT, K4, and S4

History of Relating Logic. The Origin and Research Directions

In this paper, we present the history of and the research directions in relating logic. For this purpose we will describe Epstein's Programme, which postulates accounting for the content of sentences in logical research. We will focus on analysing the content relationship and Epstein's logics that are based on it, which are special cases of relating logic. Moreover, the set-assignment semantics will be discussed. Next, the Torunian Programme of Relating Semantics will be presented; this programme explores the various non-logical relationships in logical research, including those which are content-related. We will present a general description of relating logic and semantics as well as the most prominent issues regarding the Torunian Programme, including some of its special cases and the results achieved to date

A fundamental non-classical logic

We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Arguably neither Reiteration nor Reductio is as intimately related to the meaning of the connectives as the introduction and elimination rules are, so the base logic we identify serves as a more fundamental starting point and common ground between proponents of intuitionistic logic, orthologic, and classical logic. The algebraic semantics for the logic we motivate proof-theoretically is based on bounded lattices equipped with what has been called a weak pseudocomplementation. We show that such lattice expansions are representable using a set together with a reflexive binary relation satisfying a simple first-order condition, which yields an elegant relational semantics for the logic. This builds on our previous study of representations of lattices with negations, which we extend and specialize for several types of negation in addition to weak pseudocomplementation; in an appendix, we further extend this representation to lattices with implications. Finally, we discuss adding to our logic a conditional obeying only introduction and elimination rules, interpreted as a modality using a family of accessibility relations.Comment: added topological representation of bounded lattices with implications in Appendi

Multi-Modular Integral Pressurized Water Reactor Control and Operational Reconfiguration for a Flow Control Loop

This dissertation focused on the IRIS design since this will likely be one of the designs of choice for future deployment in the U.S and developing countries. With a net 335 MWe output IRIS novel design falls in the “medium” size category and it is a potential candidate for the so called modular reactors, which may be appropriate for base load electricity generation, especially in regions with smaller electricity grids, but especially well suited for more specialized non-electrical energy applications such as district heating and process steam for desalination. The first objective of this dissertation is to evaluate and quantify the performance of a Nuclear Power Plant (NPP) comprised of two IRIS reactor modules operating simultaneously with a common steam header, which in turn is connected to a single turbine, resulting in a steam-mixing control problem with respect to “load-following” scenarios, such as varying load during the day or reduced consumption during the weekend. To solve this problem a single-module IRIS SIMULINK model previously developed by another researcher is modified to include a second module and was used to quantify the responses from both modules. In order to develop research related to instrumentation and control, and equipment and sensor monitoring, the second objective is to build a two-tank multivariate loop in the Nuclear Engineering Department at the University of Tennessee. This loop provides the framework necessary to investigate and test control strategies and fault detection in sensors, equipment and actuators. The third objective is to experimentally develop and demonstrate a fault-tolerant control strategy using this loop. Using six correlated variables in a single-tank configuration, five inferential models and one Auto-Associative Kernel Regression (AAKR) model were developed to detect faults in process sensors. Once detected the faulty measurements were successfully substituted with prediction values, which would provide the necessary flexibility and time to find the source of discrepancy and resolve it, such as in an operating power plant. Finally, using the same empirical models, an actuator failure was simulated and once detected the control was automatically transferred and reconfigured from one tank to another, providing survivability to the system