Paraconsistent Weak Kleene logic is the 3-valued logic with two designated values defined through the weak Kleene tables. This paper is a first attempt to investigate PWK within the perspective and methods of abstract algebraic logic. We give a Hilbert-style system for PWK and prove a normal form theorem. We examine some algebraic structures for PWK, called involutive bisemilattices, showing that they are distributive as bisemilattices and that they form a variety, \, generated by the 3-element algebra WK; we also (...) prove that every involutive bisemilattice is representable as the Płonka sum over a direct system of Boolean algebras. We then study PWK from the viewpoint of AAL. We show that \ is not the equivalent algebraic semantics of any algebraisable logic and that PWK is neither protoalgebraic nor selfextensional, not assertional, but it is truth-equational. We fully characterise the deductive filters of PWK on members of \ and the reduced matrix models of PWK. Finally, we investigate PWK with the methods of second-order AAL—we describe the class \ of PWK-algebras, algebra reducts of basic full generalised matrix models of PWK, showing that they coincide with the quasivariety generated by WK—which differs from \—and explicitly providing a quasiequational basis for it. (shrink)
We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Płonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation.
In this contribution we will present a generalization of de Finetti's betting game in which a gambler is allowed to buy and sell unknown events' betting odds from more than one bookmaker. In such a framework, the sole coherence of the books the gambler can play with is not sucient, as in the original de Finetti's frame, to bar the gambler from a sure-win opportunity. The notion of joint coherence which we will introduce in this paper characterizes those coherent books (...) on which sure- win is impossible. Our main results provide geometric characterizations of the space of all books which are jointly coherent with a xed one. As a consequence we will also show that joint coherence is decidable. (shrink)
Płonka sums consist of an algebraic construction similar, in some sense, to direct limits, which allows to represent classes of algebras defined by means of regular identities. Recently, Płonka sums have been connected to logic, as they provide algebraic semantics to logics obtained by imposing a syntactic filter to given logics. In this paper, I present a very general topological duality for classes of algebras admitting a Płonka sum representation in terms of dualisable algebras.
In this article, the theory of argumentation set out by the Dutch scholars Frans van Eemeren and Rob Grootendorst is brought to bear in subjecting the general form of the argument from coherence to a critical analysis. First, a distinction is brought out between two basic kinds of argument from coherence: in one use this argumentative structure occurs as a sequence of two arguments establishing that a standpoint constitutes a particular instantiation or a inherent quality of the system it will (...) become part of (symptomatic argument); in the other use we have a main symptomatic argument supported by a subordinate argument appealing to instrumental considerations (pragmatic argument). It is then claimed that arguments from coherence are complex types of argumentation, structured at various argumentative levels, where the premises must be taken together to yield an adequate defence of the conclusion (coordinative argumentation). Finally, an evaluative assessment is made as to whether arguments from coherence can serve acceptably as tools for settling disputes: it will be maintained that we can generally welcome these argumentative structures as sound and fully acceptable provided we are aware of the interpretive discretion their use entails. (shrink)
In this paper we present a method to reduce the decision problem of several infinite-valued propositional logics to their finite-valued counterparts. We apply our method to Łukasiewicz, Gödel and Product logics and to some of their combinations. As a byproduct we define sequent calculi for all these infinite-valued logics and we give an alternative proof that their tautology problems are in co-NP.
Das in Zusammenarbeit der Westfälischen Wilhelms-Universität Münster und der Ungarischen Akademie in Rom im Oktober 1996 durchgeführte internationale Symposium war den Forschungen der letzten Jahrzehnte zu S. Stefano Rotondo in Rom gewidmet. Der daraufhin publizierte Tagungsband präsentiert neben den Ergebnissen der Bauuntersuchung der frühchristlichen Kirche Beobachtungen zu Materialverwendung und Bautechnik, Beiträge zur Ausstattung des Baus und deren Restaurierung, sowie kunsthistorische Studien zur neuzeitlichen Malerei und Plastik und historische Abhandlungen zur spätmittelalterlichen und neuzeitlichen Nutzungsgeschichte und zum spezifischen Verhältnis der Ungarn (...) zu S. Stefano Rotondo und zu Rom. Sie sind in vier Abschnitten versammelt: I. Archäologie und Baugeschichte: C. Pavolini, La sommità del Celio in età imperiale: dai culti pagani orientali al culto cristiano ; E. Lissi Caronna, Edifici, fasi edilizie, demolizioni, riempimenti nell'area della basilica di Santo Stefano Rotondo ; H. Brandenburg, S. Stefano Rotondo, der letzte Großbau der Antike in Rom. Die Typologie des Baues, die Ausstattung der Kirche, die kunstgeschichtliche Stellung des Kirchenbaues und seiner Ausstattung ; P. Pensabene, Trasformazione urbana e reimpiego a Roma tra la seconda metà del IV e i primi decenni del V secolo ; K. Ringle – S. Landes, Der Einsatz der Photogrammetrie bei der Aufnahme der Kirche in S. Stefano Rotondo in Rom . II. Kunstgeschichte und Architektur: M. Nimmo, S. Stefano: la recinzione dell'altare di mezzo ; V. Biermann, Die Vita der heiligen Paulus von Theben und Stephanus: Ein neuentdeckter monochromer Gemäldezyklus des 16. Jahrhunderts in der Portikus von S. Stefano Rotondo in Rom ; L. Salviucci Insolera, Gli affreschi del ciclo dei martiri commissionati al Pomarancio in rapporto alla situazione religiosa ed artistica della seconda metà del Cinquecento . III. Restaurierung: M. Lolli-Ghetti, Basilica di S. Stefano Rotondo, Capella dei SS. Primo e Feliciano, restauro della pavimentazione paleocristiana in opus sectile ; M.G. Filetici, Il restauro del mitreo di Santo Stefano Rotondo nel quadro degli interventi di conservazione dei monumenti archeologici al Celio ; G. Basile, Il restauro del mosaico absidale della Capella dei Santi Primo e Feliciano in Santo Stefano Rotondo a Roma . IV. Geschichte: J. Krähling, László Gerö und die Basilika Santo Stefano Rotondo ; J. Pál, La fondazione del primo Collegio Ungarico a Roma ; Á. Vladár, Sulla importanza e sul ruolo determinante della chiesa Santo Stefano Rotondo nella storia degli Ungheresi ; A. Kubinyi, Ungarn in Rom im Spätmittelalter ; P. Sárközy, Il Santo Stefano Rotondo nella storia culturale ungherese ; L. Weinrich, Der Pönitentiar Valentin und die Paulinermönche in S. Stefano Rotondo. (shrink)
Kant introduces autonomy in the Groundwork of the Metaphysics of Morals as "the characteristic of the will by which it is a law to itself". Autonomy is Kant's solution to a puzzle about how to describe and account for moral obligation, which binds necessarily and cannot, therefore, be derived from any independent desire or interest. But Kant's pithy description of autonomy raises more questions than it settles. How is self-legislation possible in the first place? How is autonomy related to the (...) various imperatival statements of the moral law in the Groundwork? How can rational agents be motivated by their recognition of obligation in the absence of some other interest?Though the title of the volume... (shrink)
The editors of this bulky volume tell us that an issue of the Stanford Humanities Review ‘constituted the seed of the project that culminated in this book’ (vii). They don’t say that it was the Spring 1995 issue of that pioneering open-access e-journal, nor do they tell us how many or which of the 19 papers in this book derive from it. But since that issue is still online (as at August 28, 2006), at http://www.stanford.edu/group/SHR/4-2/text/toc.html, any reader can see that (...) 12 of its 15 papers have been reprinted almost unaltered here, a decade later, while in addition almost all of the editors’ 1995 introduction appears again in their expanded text. (shrink)
Di Bella and Schmaltz write in their introduction that the early modern problem of universals originates largely in a turn away from ancient and late-medieval problems. The modern problem, they suggest, investigates universals by asking what it means to include them as contents of our thoughts. The collection of essays that follows demonstrates persuasively, however, that we should resist the impulse, no matter how heuristic, to regard each era as having its own—much less a single—problem of universals. Despite the variety (...) and interest of other contributions to the collection, I focus here on essays that display greater continuity among the eras, and on two essays addressing thinkers whose position on... (shrink)
Upshot: Written by recognized experts in their fields, the book is a set of essays that deals with the influences of early cybernetics, computational theory, artificial intelligence, and connectionist networks on the historical development of computational-representational theories of cognition. In this review, I question the relevance of computability arguments and Jonasian phenomenology, which has been extensively invoked in recent discussions of autopoiesis and Ashby’s homeostats. Although the book deals only indirectly with constructivist approaches to cognition, it is useful reading for (...) those interested in machine-based models of mind. (shrink)