An Introduction to Critical Thinking and Symbolic Logic Volume 1: Formal Logic

This textbook has developed over the last few years of teaching introductory symbolic logic and critical thinking courses. It has been truly a pleasure to have benefited from such great students and colleagues over the years. As we have become increasingly frustrated with the costs of traditional logic textbooks (though many of them deserve high praise for their accuracy and depth), the move to open source has become more and more attractive. We're happy to provide it free of charge for educational use. With that being said, there are always improvements to be made here and we would be most grateful for constructive feedback and criticism. We have chosen to write this text in LaTex and have adopted certain conventions with symbols. Certainly many important aspects of critical thinking and logic have been omitted here, including historical developments and key logicians, and for that we apologize. Our goal was to create a textbook that could be provided to students free of charge and still contain some of the more important elements of critical thinking and introductory logic. To that end, an additional benefit of providing this textbook as a Open Education Resource (OER) is that we will be able to provide newer updated versions of this text more frequently, and without any concern about increased charges each time. We are particularly looking forward to expanding our examples, and adding student exercises. We will additionally aim to continually improve the quality and accessibility of our text for students and faculty alike. We have included a bibliography that includes many admirable textbooks, all of which we have benefited from. The interested reader is encouraged to consult these texts for further study and clarification. These texts have been a great inspiration for us and provide features to students that this concise textbook does not. We would both like to thank the philosophy students at numerous schools in the Puget Sound region for their patience and helpful suggestions. In particular, we would like to thank our colleagues at Green River College, who have helped us immensely in numerous different ways. Please feel free to contact us with comments and suggestions. We will strive to correct errors when pointed out, add necessary material, and make other additional and needed changes as they arise. Please check back for the most up to date version

Saving behaviour and global imbalances: the role of emerging market economies

In recent years there has been considerable variation in savings patterns across countries and regions, with implications for the configuration of global current account balances, asset valuations and real interest rates. This paper looks at the empirical drivers behind these trends. It uses a reduced-form model that relates private savings to a set of economic fundamentals, while controlling for structural and institutional differences across countries. Addressing a typical shortcoming of the previous literature, estimates are obtained from a dynamic model, which accounts for cross-sectional heterogeneity. The results suggest that saving rates in emerging economies are higher than cross-country estimates based on fundamentals, particularly in Asia. Demographic factors and financial catching-up have been key drivers of the observed changes in savings in these economies. Looking ahead, the prospective population aging is likely to lead to a considerable fall in saving rates in many economies - albeit the process will take decades to unfold. Further progress in financial deepening in developing economies may be conducive to a redistribution of international saving flows and may potentially support a smoother adjustment of global imbalances. JEL Classification: E20, E60emerging economies, global imbalances, panel error correction model, pooled mean group estimation, Private savings

The sustainability of China's exchange rate policy and capital account liberalisation.

This paper deals with two related issues: the sustainability of China’s exchange rate regime and the opening up of its capital account. The exchange rate discussion deliberately passes over the issue of the “equilibrium” value of the renminbi and its alleged undervaluation – typically at the heart of the current policy debate – and focuses instead on the domestic costs of the current regime and the potential risks to domestic financial stability in the long run. The paper argues that the renminbi exchange rate should be increasingly determined by market forces and that administrative controls should be progressively relinquished. The exchange rate is obviously linked to well-functioning and efficient capital markets, which require no barriers to capital flows. Thus, exchange rate reform has to be correctly sequenced with reform of the capital account to avoid disruptive capital flows. The paper discusses China’s twin surpluses of the current and capital accounts and attempts to identify the drivers of this “anomalous” external position. The pragmatic strategy pursued by the Chinese authorities in the aftermath of the Asian crisis encouraged FDI inflows and favoured the accumulation of a large stock of foreign exchange reserves. Combined with a relatively weak institutional setting, these factors have been important determinants of the pattern and composition of the country’s capital flows and international investment position. Finally, the paper speculates on the outlook for Chinese capital flows should barriers to capital movements be lifted. It argues that whether China continues to supply capital to the rest of the world or eventually becomes a net borrower in international capital markets – as was the case for most of its recent history – will depend on the evolution of its institutions. JEL Classification: F10, F21, F31, F32, P48.China, exchange rate policy, international investment position, capital account liberalisation, institutions.

An LTL Semantics of Business Workflows with Recovery

We describe a business workflow case study with abnormal behavior management (i.e. recovery) and demonstrate how temporal logics and model checking can provide a methodology to iteratively revise the design and obtain a correct-by construction system. To do so we define a formal semantics by giving a compilation of generic workflow patterns into LTL and we use the bound model checker Zot to prove specific properties and requirements validity. The working assumption is that such a lightweight approach would easily fit into processes that are already in place without the need for a radical change of procedures, tools and people's attitudes. The complexity of formalisms and invasiveness of methods have been demonstrated to be one of the major drawback and obstacle for deployment of formal engineering techniques into mundane projects

On Redundancy Elimination Tolerant Scheduling Rules

In (Ferrucci, Pacini and Sessa, 1995) an extended form of resolution, called Reduced SLD resolution (RSLD), is introduced. In essence, an RSLD derivation is an SLD derivation such that redundancy elimination from resolvents is performed after each rewriting step. It is intuitive that redundancy elimination may have positive effects on derivation process. However, undesiderable effects are also possible. In particular, as shown in this paper, program termination as well as completeness of loop checking mechanisms via a given selection rule may be lost. The study of such effects has led us to an analysis of selection rule basic concepts, so that we have found convenient to move the attention from rules of atom selection to rules of atom scheduling. A priority mechanism for atom scheduling is built, where a priority is assigned to each atom in a resolvent, and primary importance is given to the event of arrival of new atoms from the body of the applied clause at rewriting time. This new computational model proves able to address the study of redundancy elimination effects, giving at the same time interesting insights into general properties of selection rules. As a matter of fact, a class of scheduling rules, namely the specialisation independent ones, is defined in the paper by using not trivial semantic arguments. As a quite surprising result, specialisation independent scheduling rules turn out to coincide with a class of rules which have an immediate structural characterisation (named stack-queue rules). Then we prove that such scheduling rules are tolerant to redundancy elimination, in the sense that neither program termination nor completeness of equality loop check is lost passing from SLD to RSLD.Comment: 53 pages, to appear on TPL

Projections of SDEs onto Submanifolds

In [AB16] the authors define three projections of $\mathbb R^d$-valued stochastic differential equations (SDEs) onto submanifolds: the Stratonovich, It\^o-vector and It\^o-jet projections. In this paper, after a brief survey of SDEs on manifolds, we begin by giving these projections a natural, coordinate-free description, each in terms of a specific representation of manifold-valued SDEs. We proceed by deriving formulae for the three projections in ambient $\mathbb R^d$-coordinates. We use these to show that the It\^o-vector and It\^o-jet projections satisfy respectively a weak and mean-square optimality criterion "for small t": this is achieved by solving constrained optimisation problems. These results confirm, but do not rely on the approach taken in [AB16], which is formulated in terms of weak and strong It\^o-Taylor expansions. In the final section we exhibit examples showing how the three projections can differ, and explore alternative notions of optimality

Non-null Infinitesimal Micro-steps: a Metric Temporal Logic Approach

Many systems include components interacting with each other that evolve with possibly very different speeds. To deal with this situation many formal models adopt the abstraction of "zero-time transitions", which do not consume time. These however have several drawbacks in terms of naturalness and logic consistency, as a system is modeled to be in different states at the same time. We propose a novel approach that exploits concepts from non-standard analysis to introduce a notion of micro- and macro-steps in an extension of the TRIO metric temporal logic, called X-TRIO. We use X-TRIO to provide a formal semantics and an automated verification technique to Stateflow-like notations used in the design of flexible manufacturing systems.Comment: 20 pages, 2 figures, submitted to the conference "FORMATS: Formal Modelling and Analysis of Timed Systems" 201