We start with a simple proof of Leivant's normal form theorem for ∑11 formulas over finite successor structures. Then we use that normal form to prove the following:1. over all finite structures, every ∑21 formula is equivalent to a ∑21 formula whose first-order part is a Boolean combination of existential formulas, and2. over finite successor structures, the Kolaitis-Thakur hierarchy of minimization problems collapses completely and the Kolaitis-Thakur hierarchy of maximization problems collapses partially.The normal form theorem for ∑21 fails if ∑21 (...) is replaced with ∑11 or if infinite structures are allowed. (shrink)

As is well known, answer-set programs do not satisfy the replacement property in general, i.e., programs and that are equivalent may cease to be so when they are put in the context of some other program, i.e., and may have different answer sets. Lifschitz, Pearce, and Valverde thus introduced strong equivalence for context-independent equivalence, and proved that such equivalence holds between given programs and iff and are equivalent theories in the monotonic logic of here-and-there. In this article, we consider a (...) related question: given a program, does there exist some program from a certain class of programs such that and are equivalent under a given notion of equivalence? Furthermore, if the answer to this question is positive, how can we recast as an equivalent program from? In particular, we consider classes of programs that emerge by allowing disjunction and/or negation, and as equivalence notions we consider strong, uniform, and ordinary equivalence. Based on general model-theoretic properties and a novel form of canonical programs, we develop semantic characterisations for the existence of such a program, determine the computational complexity of checking existence, and provide rewriting rules for recasting. (shrink)

It was conjectured by Halpern and Kapron (Annals of Pure and Applied Logic, vol. 69, 1994) that frame satisfiability of propositional modal formulas is incomparable in expressive power to both Σ 1 1 (Ackermann) and Σ 1 1 (Bernays-Schonfinkel). We prove this conjecture. Our results imply that Σ 1 1 (Ackermann) and Σ 1 1 (Bernays-Schonfinkel) are incomparable in expressive power, already on finite graphs. Moreover, we show that on ordered finite graphs, i.e., finite graphs with a successor, Σ 1 (...) 1 (Bernays-Schonfinkel) is strictly more expressive than Σ 1 1 (Ackermann). (shrink)

Big Ideas for Little Kids includes everything a teacher, a parent, or a college student needs to teach philosophy to elementary school children from picture books. Written in a clear and accessible style, the book explains why it is important to allow young children access to philosophy during primary-school education. Wartenberg also gives advice on how to construct a "learner-centered" classroom, in which children discuss philosophical issues with one another as they respond to open-ended questions by saying whether they agree (...) or disagree with what others have said. (shrink)

v. 1. Editorial introduction -- v. 2. The English and Latin texts (i) -- v. 3. The English and Latin texts (ii).

In this book, T. M. Scanlon offers new answers to these questions, as they apply to the central part of morality that concerns what we owe to each other.

This paper is an exposition and evaluation of the Agustín Rayo's views about the epistemology and metaphysics of mathematics, as they are presented in his book The Construction of Logical Space.

This volume is a study of the influence of Timaeus on the development of Western cosmology in three axial periods of European culture: Late Antiquity, Middle Ages and Renaissance.

Thomas Reid is now recognized as one of the towering figures of the Enlightenment. Best known for his published writings on epistemology and moral theory, he was also an accomplished mathematician and natural philosopher, as an earlier volume of his manuscripts edited by Paul Wood for the Edinburgh Reid Edition, Thomas Reid on the Animate Creation, has shown. The Correspondence of Thomas Reid collects all of the known letters to and from Reid in a fully annotated form. (...) Letters already published by Sir William Hamilton and others have been reedited, and roughly half of the letters included appear in print for the first time. Writing in 1802, Reid's disciple and biographer Dugald Stewart doubted that Reid's correspondence &"would be generally interesting.&" This collection proves otherwise, for the letters illuminate virtually every aspect of Reid's life and career and, in some instances, provide us with invaluable evidence about activities otherwise undocumented in his manuscripts or published works. Through his correspondence we can trace Reid's relations with contemporaries such as David Hume and his colleagues at both King's College, Aberdeen, and the University of Glasgow, as well as his engagement with the most controversial philosophical, scientific, and political issues of his day. If anything, the letters assembled here serve as the starting point for understanding Reid and his place in the Enlightenment. (shrink)

Feeling good: four ways -- Finding that feeling -- The place of pleasure -- Knowing what's what -- Making things happen -- Being good -- Love and friendship -- Putting it together.