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.

In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in m. We also reduce the notion of logical consequence in to the same (...) notion in a suitable finite set of finite-valued ukasiewicz logics. Finally, we define an analytic and internal sequent calculus for infinite-valued ukasiewicz logic. (shrink)

We extend de Finetti’s No-Dutch-Book Criterion to Gödel infinite-valued propositional logic.

For each integer n≥0, we provide an explicit functional characterization of the free n-generated BL-algebra, together with an explicit construction of the corresponding normal forms.

We extend de Finetti's No-Dutch-Book Criterion to Gödel infinite-valued propositional logic.

We axiomatize the notion of state over finitely generated free NM-algebras, the Lindenbaum algebras of pure Nilpotent Minimum logic. We show that states over the free n -generated NM-algebra exactly correspond to integrals of elements of with respect to Borel probability measures.

Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom =. In 1969, Horn proved that a Heyting algebra is a Gödel algebra if and only if its set of prime filters partially ordered by reverse inclusion–i.e. its prime spectrum–is a forest. Our main result characterizes Gödel algebras that are free over some finite distributive lattice by an intrisic property of their spectral forest.

In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas (...) can be interpreted as modal formulas over a flow of time, where the logic of each instant is Łukasiewicz, with a finite or infinite number of truth values. As a main result, we obtain validity with respect to all flows of times that are non-branching to the future, and completeness with respect to all finite linear flows of time, or to an appropriate single infinite linear flow of time. It may be argued that this reduces the problem of establishing a meaningful interpretation of the truth values in BL logic to the analogous problem for Łukasiewicz logic. (shrink)

The aim of the paper is to shed light on some of the most original elements of Fichte’s conception of morality as expressed in his account of specific obligations. After some remarks on Fichte’s original classification of ethical duties, the paper focuses on the prohibition of lying, the duty to communicate our true knowledge, and the duty to set a good example. Fichte’s account of those duties not only goes beyond the mere justification of universally acknowledged demands, but also deploys (...) different arguments than his contemporaries, most notably Kant. Fichte thereby sketches a conception of morality in which the agent is crucially required to contribute to the morality of others. The chapter explores the contrast between Fichte’s view and Kant’s thought of an end in itself and suggests that Fichte’s view of morality amounts to a form of normative perfectionism that is qualified by the underlying claim of the agent-neutral character of moral demands. (shrink)

My chapter deals with an important part of how Wolff pursued the normative ambitions of his ethics in giving practical guidance with regard to specific moral issues. I first consider how Wolff’s ethics tackles the duties to others, which traditionally represent a difficult issue for moral perfectionism. In this regard, I argue that Wolff’s strategy combines two aspects: (a) he includes in perfection non-active aspects and (b) operates with an agent-neutral notion of perfection, in spite of important passages that might (...) suggest differently. I then focus on Wolff’s treatment of the duties concerning veracity and lying, and show how it follows that general strategy. Combining its two aspects, Wolff examines specific moral issues by adopting a non-welfarist notion of benefit and harm as the standard that can give guidance about practical cases. (shrink)

The concern of this book is to see whether the phenomenological effervescence of politics is still possible to retrace the nucleolus of the political in its archetypical form.

This book argues against the widely celebrated utopia of -transparency- by showing, across a panorama of postwar French thought, how attempts to show the perils of transparency in politics, ethics, and knowledge led to major conceptual inventions, many of which we now take for granted.

Die Epitome physica des Nikephoros Blemmydes (1197 – nach 1269) gilt als eines der meistverbreiteten Lehrbücher aristotelischer Naturphilosophie in der byzantinischen und nachbyzantinischen Welt. Dennoch blieb die handschriftliche Überlieferung bisher gänzlich unerforscht und der Text wurde nie in Form einer kritischen Edition zugänglich gemacht. Die Epitome physica stellt das zweite Buch der Εἰσαγωγικὴ ἐπιτομή (Einführendes Kompendium) dar, deren erstes Buch der Logik gewidmet ist. Als Grundlage dienten Blemmydes im Wesentlichen Aristoteles und seine Kommentatoren (sowie für den astronomischen Teil den Stoiker (...) Kleomedes), wobei er versuchte, eine Synthese der antiken Naturphilosophie mit der christlichen Weltanschauung zu erreichen. Von den über 120 erhaltenen Manuskripten der Epitome, die vom 13. bis ins 19 Jh. datieren, werden im vorliegenden Buch die Handschriften aus der Palaiologenzeit sowie die Mehrheit derjenigen aus der Renaissance manuskriptologisch und philologisch untersucht sowie ihre textgeschichtlichen Beziehungen rekonstruiert. Daneben kommen auch die Verbreitung und der kulturelle Stellenwert der Epitome physica in der byzantinischen Welt und in der europäischen Renaissance zur Darstellung. (shrink)

1. Sviluppi critici della fenomenologia.--2. Fenomenologia e sapere scientifico.

The five-volume set Kant and Philosophy in a Cosmopolitan Sense contains the proceedings of the Eleventh International Kant Congress, which took place in Pisa in 2010. The proceedings consist of 25 plenary talks and 341 papers selected by a team of international referees from over 700 submissions. The contributions span 14 sections: Kant’s Concept of Philosophy; Theory of Cognition and Logic; Ontology and Metaphysics; Ethics; Law and Justice; Religion and Theology; Aesthetics; Anthropology and Psychology; Politics and History; Science, Mathematics, and (...) the Philosophy of Nature; Kant and the Leibnizian Tradition; Kant and the Philosophical Tradition; Kant and Schopenhauer; and Kant’s Heritage. Thanks to cooperation from the Schopenhauer Gesellschaft, the 2010 conference was the first in the history of the International Kant Congress to include a session on Kant and Schopenhauer. -/- . (shrink)

The set of unary functions of complexity classes defined by using bounded primitive recursion is inductively characterized by means of bounded iteration. Elementary unary functions, linear space computable unary functions and polynomial space computable unary functions are then inductively characterized using only composition and bounded iteration.

I present a novel explanation of the apparent truth of certain remarks about fiction, such as an utterance of ''Salieri commissioned the Requiem'' during a discussion of the movie Amadeus. I criticize the traditional view, which alleges that the uttered sentence abbreviates the longer sentence ''it is true in the movie Amadeus that Salieri commissioned the Requiem''. I propose a solution which appeals to some independently motivated results concerning the contexts relevant for the semantic evaluation of indexical expressions.

This book explores what it means to exist in virtual worlds. Chiefly drawing on the philosophical traditions of existentialism, it articulates the idea that — by means of our technical equipment and coordinated practices — human beings disclose contexts or worlds in which they can perceive, feel, act, and think. More specifically, this book discusses how virtual worlds allow human beings to take new perspectives on their values and beliefs, and explore previously unexperienced ways of being. Virtual Existentialism will be (...) useful for scholars working in the fields of philosophy, anthropology, media studies, and digital game studies. (shrink)

While agent-based modelling languages naturally implement concurrency, the currently available languages for argumentation do not allow to explicitly model this type of interaction. In this paper we introduce a concurrent language for handling agents arguing and communicating using a shared argumentation space. We also show how to perform high-level operations like persuasion and negotiation through basic belief revision constructs, and present a working implementation of the language and the associated web interface.

Iterative characterizations of computable unary functions are useful patterns for the definition of programming languages based on iterative constructs. The features of such a characterization depend on the pairing producing it: this paper offers an infinite class of pairings involving very nice features.

The set, the closure of F, is the closure with respect to substitution and concatenation recursion on notation of a set of basic functions comprehending the set F. By improving earlier work, we show that is the substitution closure of a simple function set and characterize well‐known function complexity classes as the substitution closure of finite sets of simple functions.