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)
In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL  plays a major rôle. The completeness theorem proved in  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)
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 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 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)
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)
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)
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)