We develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of the Blok–Esakia (...) theorem and the theory of modal companions to systems of multiple-conclusion rules or (finitary structural global) consequence relations, and a characterization of splittings in the lattices of consequence relations over monomodal or superintuitionistic logics with the finite model property. (shrink)

We study the notion of conservative translation between logics introduced by (Feitosa & D’Ottaviano2001). We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most (...) nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal. (shrink)

One of the major works of the great German theologian Emil Brunner, The Divine Imperative deals with what we ought to do. People are unconvinced that there is an inviolable moral obligation governing human life because they do not believe that the 'good'can be precisely and clearly known. Haven't some generations called bad what others have called good? Aren't moral standards relative? Doesn't religion lack uniform and practical moral guidance? Brunner discusses the moral confusion we face. He analyses the (...) nature of the Good, showing why the Christian faith as understood by the Protestant Reformers provides the only true approach and answer to the ethical problem. Philosophical ethics, whether ancient or modern, cannot correctly define the Good, becausethe Good is regarded either as too abstract and absolute or as too concrete and relative. Christianity, by contrast, sees the moral problem as one of responsibility between humans who are created so as to respond to God. He created men for responsive fellowship with Him, establishing orderly ways of acting in the world. Correct understanding of the nature of society, family, state, economic life, is needed to discern one's duty. Because Brunner's analysis is at once fundamental and comprehensive, this book remains a fresh and compelling treatment of the moral problem. It offers a provocative discussion and solution of a perennial human problem. (shrink)

We show that the universally axiomatized, induction-free theory equation image is a sequential theory in the sense of Pudlák's 5, in contrast to the closely related Robinson's arithmetic.

We formalize the construction of Paterson’s variant of the Ajtai–Komlós–Szemerédi sorting network of logarithmic depth in the bounded arithmetical theory , under the assumption of the existence of suitable expander graphs. We derive a conditional p-simulation of the propositional sequent calculus in the monotone sequent calculus.

D’Aquino et al. (J Symb Log 75(1):1–11, 2010) have recently shown that every real-closed field with an integer part satisfying the arithmetic theory IΣ4 is recursively saturated, and that this theorem fails if IΣ4 is replaced by IΔ0. We prove that the theorem holds if IΣ4 is replaced by weak subtheories of Buss’ bounded arithmetic: PV or $${\Sigma^b_1-IND^{|x|_k}}$$. It also holds for IΔ0 (and even its subtheory IE 2) under a rather mild assumption on cofinality. On the other hand, it (...) fails for the extension of IOpen by an axiom expressing the Bézout property, even under the same assumption on cofinality. (shrink)

Grzegorczyk's modal logic corresponds to the class of upwards well-founded partially ordered Kripke frames, however all known proofs of this fact utilize some form of the Axiom of Choice; G. Boolos asked in [1], whether it is provable in plain ZF. We answer his question negatively: Grz corresponds to a class of frames, which does not provably coincide with upwards well-founded posets in ZF alone.

Atserias, Galesi, and Pudlák have shown that the monotone sequent calculus MLK quasipolynomially simulates proofs of monotone sequents in the full sequent calculus LK . We generalize the simulation to the fragment MCLK of LK which can prove arbitrary sequents, but restricts cut-formulas to be monotone. We also show that MLK as a refutation system for CNFs quasipolynomially simulates LK.

This paper examines the characteristics of infectious diseases that raise special medical and social ethical issues, and explores ways of integrating both current bioethical and classical public health ethics concerns. Many of the ethical issues raised by infectious diseases are related to these diseases' powerful ability to engender fear in individuals and panic in populations. We address the association of some infectious diseases with high morbidity and mortality rates, the sense that infectious diseases are caused by invasion or attack on (...) humans by foreign micro-organisms, the acute onset and rapid course of many infectious diseases, and, in particular, the communicability of infectious diseases. The individual fear and community panic associated with infectious diseases often leads to rapid, emotionally driven decision making about public health policies needed to protect the community that may be in conflict with current bioethical principles regarding the care of individual patients. The discussion includes recent examples where dialogue between public health practitioners and medical-ethicists has helped resolve ethical issues that require us to consider the infected patient as both a victim with individual needs and rights and as a potential vector of disease that is of concern to the community. (shrink)

The redundant-signals paradigm (RSP) is designed to investigate response behavior in perceptual tasks in which response-relevant targets are defined by either one or two features, or modalities. The common finding is that responses are speeded for redundantly compared to singly defined targets. This redundant-signals effect (RSE) can be accounted for by race models if the response times do not violate the race model inequality (RMI). When there are violations of the RMI, race models are effectively excluded as a viable account (...) of the RSE. The common alternative is provided by co-activation accounts, which assume that redundant target signals are integrated at some processing stage. However, ‘co-activation’ has mostly been only indirectly inferred and the accounts have only rarely been explicitly modeled; if they were modeled, the RSE has typically been assumed to have a decisional locus. Yet, there are also indications in the literature that the RSE might originate, at least in part, at a non-decisional or motor stage. In the present study, using a distribution analysis of sequential-sampling models (ex-Wald and Ratcliff Diffusion model), the locus of the RSE was investigated for two bimodal (audio-visual) detection tasks that strongly violated the RMI, indicative of substantial co-activation. Three model variants assuming different loci of the RSE were fitted to the quantile reaction time proportions: a decision, a non-decision, and a combined variant both to vincentized group as well as individual data. The results suggest that for the two bimodal detection tasks, co-activation has a shared decisional and non-decisional locus. These findings point to the possibility that the mechanisms underlying the RSE depend on the specifics (task, stimulus, conditions, etc.) of the experimental paradigm. (shrink)

We introduce a nonstandard arithmetic $NQA^-$ based on the theory developed by R. Chuaqui and P. Suppes in [2] (we will denote it by $NQA^+$ ), with a weakened external open minimization schema. A finitary consistency proof for $NQA^-$ formalizable in PRA is presented. We also show interesting facts about the strength of the theories $NQA^-$ and $NQA^+$ ; $NQA^-$ is mutually interpretable with $I\Delta_0 + EXP$ , and on the other hand, $NQA^+$ interprets the theories IΣ1 and $WKL_0$.

This paper examines the characteristics of infectious diseases that raise special medical and social ethical issues, and explores ways of integrating both current bioethical and classical public health ethics concerns. Many of the ethical issues raised by infectious diseases are related to these diseases’ powerful ability to engender fear in individuals and panic in populations. We address the association of some infectious diseases with high morbidity and mortality rates, the sense that infectious diseases are caused by invasion or attack on (...) humans by foreign micro‐organisms, the acute onset and rapid course of many infectious diseases, and, in particular, the communicability of infectious diseases. The individual fear and community panic associated with infectious diseases often leads to rapid, emotionally driven decision making about public health policies needed to protect the community that may be in conflict with current bioethical principles regarding the care of individual patients. The discussion includes recent examples where dialogue between public health practitioners and medical‐ethicists has helped resolve ethical issues that require us to consider the infected patient as both a victim with individual needs and rights and as a potential vector of disease that is of concern to the community. (shrink)

The first attempt at a systematic approach to axiomatic theories of truth was undertaken by Friedman and Sheard (Ann Pure Appl Log 33:1–21, 1987). There twelve principles consisting of axioms, axiom schemata and rules of inference, each embodying a reasonable property of truth were isolated for study. Working with a base theory of truth conservative over PA, Friedman and Sheard raised the following questions. Which subsets of the Optional Axioms are consistent over the base theory? What are the proof-theoretic strengths (...) of the consistent theories? The first question was answered completely by Friedman and Sheard; all subsets of the Optional Axioms were classified as either consistent or inconsistent giving rise to nine maximal consistent theories of truth.They also determined the proof-theoretic strength of two subsets of the Optional Axioms. The aim of this paper is to continue the work begun by Friedman and Sheard. We will establish the proof-theoretic strength of all the remaining seven theories and relate their arithmetic part to well-known theories ranging from PA to the theory of ${\Sigma^1_1}$ dependent choice. (shrink)

The dignity of the human being has gained prominence in recent years as a fundamental principle from which rights also considered fundamental are derived. Based on the discussion provoked by Luhmann on external resources to the right in a system defined as operatively closed and cognitively open, the paper asks if the dignity of human being may occupy this functional place. KEY WORDS – Human dignity. Fundamental rights. Legal sociology. Systems theory.