"Ancient philosophers were very interested in the themes of laughter, humor and comedy. They theorized about laughter and its causes, moralized about the appropriate uses of humor and what it is appropriate to laugh at, and wrote treaties on comedic composition. Further, they were often merciless in ridiculing their opponents' positions, often borrowing comedic devices and techniques from comic poetry and drama to do so. The volume is organized around three themes that were important for ancient philosophers: the psychology of (...) laughter, the ethical and social norms governing laughter and humor. and the philosophical uses of humor and comedic technique"--. (shrink)

In this paper we give a rather detailed algebraic investigation of interpolation and Beth’s property in propositional many-valued logics extending Hájek’s Basic Logic [P. Hájek, Metamathematics of Fuzzy Logic, Kluwer, 1998], and we connect such properties with amalgamation and strong amalgamation in the corresponding varieties of algebras. It turns out that, while the most interesting extensions of in the language of have deductive interpolation, very few of them have Beth’s property or Craig interpolation. Thus in the last part of the (...) paper we look for conservative extensions of having such properties. (shrink)

We investigate the variety corresponding to a logic, which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative axiomatization of such variety. We also investigate the variety, called the variety of algebras, corresponding to the logic obtained from by the adding of a constant and of a defining axiom for one half. We also connect algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that (...) every algebra can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield, and whose operations are the truncations of the operations of to [0, 1]. We prove that such a structure is uniquely determined by up to isomorphism, and we establish an equivalence between the category of algebras and that of f-semifields. (shrink)

The present paper deals with the predicate version MTL of the logic MTL by Esteva and Godo. We introduce a Kripke semantics for it, along the lines of Ono''s Kripke semantics for the predicate version of FLew (cf. [O85]), and we prove a completeness theorem. Then we prove that every predicate logic between MTL and classical predicate logic is undecidable. Finally, we prove that MTL is complete with respect to the standard semantics, i.e., with respect to Kripke frames on the (...) real interval [0,1], or equivalently, with respect to MTL-algebras whose lattice reduct is [0,1] with the usual order. (shrink)

This paper is devoted to the algebraization of an arithmetical predicate introduced by S. Feferman. To this purpose we investigate the equational class of Boolean algebras enriched with an operation (g=rtail), which translates such predicate, and an operation τ, which translates the usual predicate Theor. We deduce from the identities of this equational class some properties of (g=rtail) and some ties between (g=rtail) and τ; among these properties, let us point out a fixed-point theorem for a sufficiently large class of (...) (g=rtail)-τ polynomials. The last part of this paper concerns the duality theory for (g=rtail)-τ algebras. (shrink)

This paper deals with Kripke-style semantics for many-valued logics. We introduce various types of Kripke semantics, and we connect them with algebraic semantics. As for modal logics, we relate the axioms of logics extending MTL to properties of the Kripke frames in which they are valid. We show that in the propositional case most logics are complete but not strongly complete with respect to the corresponding class of complete Kripke frames, whereas in the predicate case there are important many-valued logics (...) like BL, Ł and Π, which are not even complete with respect to the class of all predicate Kripke frames in which they are valid. Thus although very natural, Kripke semantics seems to be slightly less powerful than algebraic semantics. (shrink)

The thesis of this article is that engagement and suffering are essential aspects of responsible caregiving. The sense of medical responsibility engendered by engaged caregiving is referred to herein as clinical phronesis, i.e. practical wisdom in health care, or, simply, practical health care wisdom. The idea of clinical phronesis calls to mind a relational or communicative sense of medical responsibility which can best be understood as a kind of virtue ethics, yet one that is informed by the exigencies of moral (...) discourse and dialogue, as well as by the technical rigors of formal reasoning. The ideal of clinical phronesis is not (necessarily) contrary to the more common understandings of medical responsibility as either beneficence or patient autonomy — except, of course, when these notions are taken in their disengaged form (reflecting the malaise of modern medicine). Clinical phronesis, which gives rise to a deeper, broader, and richer, yet also to a more complex, sense than these other notions connote, holds the promise both of expanding, correcting, and perhaps completing what it currently means to be a fully responsible health care provider. In engaged caregiving, providers appropriately suffer with the patient, that is, they suffer the exigencies of the patient's affliction (though not his or her actual loss) by consenting to its inescapability. In disengaged caregiving — that ruse Katz has described as the silent world of doctor and patient — provides may deny or refuse any given connection with the patient, especially the inevitability of the patient's affliction and suffering (and, by parody of reasoning, the inevitability of their own. When, however, responsibility is construed qualitatively as an evaluative feature of medical rationality, rather than quantitatively as a form of calculative reasoning only, responsibility can be viewed more broadly as not only a matter of science and will, but of language and communication as well — in particular, as the task of responsibly narrating and interpreting the patient's story of illness. In summary, the question is not whether phronesis can save the life of medical ethics — only responsible humans can do that! Instead, the question should be whether phronesis, as an ethical requirement of health care delivery, can prevent the death of medical ethics. (shrink)

Abstract.Given a class C of t-norm BL-algebras, one may wonder which is the complexity of the set Taut(C∀) of predicate formulas which are valid in any algebra in C. We first characterize the classes C for which Taut(C∀) is recursively axiomatizable, and we show that this is the case iff C only consists of the Gödel algebra on [0,1]. We then prove that in all cases except from a finite number Taut(C∀) is not even arithmetical. Finally we consider predicate monadic (...) logics TautM(C∀) of classes C of t-norm BL-algebras, and we prove that (possibly with finitely many exceptions) they are undecidable. (shrink)

The modern West has vigorously sought to overcome death, or at the very least minimize the suffering that it entails. Whereas the former has been predominantly pursued through modern scientific medicine, the minimization of the adversity of death and dying has been sought through ‘death technologies’. This technologization of death is analyzed in light of Martin Heidegger’s phenomenological philosophy. The analysis begins with an outline of the fundamental tenets of Heidegger’s ‘philosophy of Being’. In turn, his philosophical framework is utilized (...) to highlight the manner in which the technologization of dying serves to conceal the central existential questions about being and finitude that dying gives rise to. The paper concludes with a discussion of how Heidegger’s work can inspire a more authentic stance toward dying. Leo Tolstoy’s The Death of Ivan Ilych is referred to in order to illustrate Heidegger’s construal of this existential struggle toward dying. (shrink)

For every sequence |p n } n of formulas of Peano ArithmeticPA with, every formulaA of the first-order theory diagonalizable algebras, we associate a formula 0 A, called the value ofA inPA with respect to the interpretation. We show that, ifA is true in every diagonalizable algebra, then, for every, 0 A is a theorem ofPA.

In this paper we provide a categorical equivalence for the category \ of product algebras, with morphisms the homomorphisms. The equivalence is shown with respect to a category whose objects are triplets consisting of a Boolean algebra B, a cancellative hoop C and a map \ from B × C into C satisfying suitable properties. To every product algebra P, the equivalence associates the triplet consisting of the maximum boolean subalgebra B, the maximum cancellative subhoop C, of P, and the (...) restriction of the join operation to B × C. Although several equivalences are known for special subcategories of \ , up to our knowledge, this is the first equivalence theorem which involves the whole category of product algebras. The syntactic counterpart of this equivalence is a syntactic reduction of classical logic CL and of cancellative hoop logic CHL to product logic, and viceversa. (shrink)

The undecidability of the first-order theory of diagonalizable algebras is shown here.

In this paper we investigate the connections between quantifier elimination, decidability and Uniform Craig Interpolation in Δ-core fuzzy logics added with propositional quantifiers. As a consequence, we are able to prove that several propositional fuzzy logics have a conservative extension which is a Δ-core fuzzy logic and has Uniform Craig Interpolation.

A logic for classical conditional events was investigated by Dubois and Prade. In their approach, the truth value of a conditional event may be undetermined. In this paper we extend the treatment to many-valued events. Then we support the thesis that probability over partially undetermined events is a conditional probability, and we interpret it in terms of bets in the style of de Finetti. Finally, we show that the whole investigation can be carried out in a logical and algebraic setting, (...) and we find a logical characterization of coherence for assessments of partially undetermined events. (shrink)

In this paper we investigate fuzzy propositional and first order logics which are complete or strongly complete with respect to a single chain, and we relate this properties with the existence of a universal chain for the logic.

This note contains a correct proof of the fact that the set of all first-order formulas which are valid in all predicate Kripke frames for Hájek's many-valued logic BL is not arithmetical. The result was claimed in [5], but the proof given there was incorrect.

Este trabajo intenta analizar la concepción, naturaleza jurídica y garantía de los derechos económicos, sociales y culturales, en América Latina, así como las condiciones y medidas que pueden contribuir a su efectividad. Presenta también una propuesta de indicadores que pueden utilizarse en la supervisión de la efectividad de esos derechos y de la protección que ellos han alcanzado, proporcionando información sobre la situación latinoamericana y caribeña actual.

We present a complete and cut-free proof-system for a fragment of MTL, where modal operators are only labelled by bounded intervals with rational endpoints.

This paper is devoted to the algebraization of theories in which, as in Peano arithmetic, there is a formula, Theor(x), numerating the set of theorems, and satisfying Hilbert-Bernays derivability conditions. In particular, we study the diagonalizable algebras, which are been introduced by R. Magari in [6], [7]. We prove that for every natural number n, the n-freely generated algebra $\germ{J}_{n}$ is not functionally free in the equational class of diagonalizable algebras; we also prove that the diagonalizable algebra of Peano arithmetic (...) is not an element of the equational class generated by $\{\germ{J}_{n}\}$. (shrink)