•  5
    Defining Measures in a Mereological Space
    with Giuseppina Barbieri
    Logic and Logical Philosophy 1. forthcoming.
    We explore the notion of a measure in a mereological structure and we deal with the difficulties arising. We show that measure theory on connection spaces is closely related to measure theory on the class of ortholattices and we present an approach akin to Dempster’s and Shafer’s. Finally, the paper contains some suggestions for further research.
  • Inferences in probability logic
    Artificial Intelligence 70 (1-2): 33-52. 1994.
  •  7
    Fuzziness in Italy – Traces of a scattered history
    with Gianpiero Cattaneo, Giulianella Coletti, Antonio Di Nola, Mario Fedrizzi, Gabriella Pasi, Marco Elio Tabacchi, Settimo Termini, and Aldo Ventre
    Archives for the Philosophy and History of Soft Computing 2017 (1). 2017.
    The history of Fuzziness in Italy is varied and scattered among a num- ber of research groups. As a matter of fact, “fuzziness” spread in Italy through a sort of spontaneous diffusion, and, also subsequently, no one felt the need to cre- ate some “national” common structure like an Association or similar things. Since a cohesive retelling would be next to impossible, a few members of the Italian fuzzy community have been asked to recount their experience and express their hopes for the future.
  •  37
    Pointless metric spaces
    Journal of Symbolic Logic 55 (1): 207-219. 1990.
  •  25
    Effectiveness and Multivalued Logics
    Journal of Symbolic Logic 71 (1). 2006.
    Effective domain theory is applied to fuzzy logic. The aim is to give suitable notions of semi-decidable and decidable L-subset and to investigate about the effectiveness of the fuzzy deduction apparatus
  •  23
    We propose the notion of partial recursiveness and strong partial recursiveness for fuzzy maps. We prove that a fuzzy map f is partial recursive if and only if it is computable by a Turing fuzzy machine and that f is strongly partial recursive and deterministic if and only if it is computable via a deterministic Turing fuzzy machine. This gives a simple and manageable tool to investigate about the properties of the fuzzy machines
  • On the Logical Structure of Verisimilitude
    Epistemologia 12 (1): 161. 1989.
  •  19
    Mathematical Features of Whitehead’s Point-free Geometry
    with Annamaria Miranda
    In Michel Weber (ed.), Handbook of Whiteheadian Process Thought, De Gruyter. pp. 119-130. 2008.
  •  6
    A note on the principle of predication
    Notre Dame Journal of Formal Logic 23 (4): 471-472. 1982.
  •  128
    Point-Free Geometry and Verisimilitude of Theories
    Journal of Philosophical Logic 36 (6): 707-733. 2007.
    A metric approach to Popper's verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. Th…Read more
  •  37
    Connection structures
    with Loredana Biacino
    Notre Dame Journal of Formal Logic 32 (2): 242-247. 1991.
    Whitehead, in his famous book "Process and Reality", proposed a definition of point assuming the concepts of “region” and “connection relation” as primitive. Several years after and independently Grzegorczyk, in a brief but very interesting paper proposed another definition of point in a system in which the inclusion relation and the relation of being separated were assumed as primitive. In this paper we compare their definitions and we show that, under rather natural assumptions, they coincide.
  •  19
    Pavelka's Fuzzy Logic and Free L-Subsemigroups
    Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (7-8): 123-129. 1985.
  •  274
    Whitehead's pointfree geometry and diametric posets
    with Bonaventura Paolillo
    Logic and Logical Philosophy 19 (4): 289-308. 2010.
    This note is motivated by Whitehead’s researches in inclusion-based point-free geometry as exposed in An Inquiry Concerning the Principles of Natural Knowledge and in The concept of Nature. More precisely, we observe that Whitehead’s definition of point, based on the notions of abstractive class and covering, is not adequate. Indeed, if we admit such a definition it is also questionable that a point exists. On the contrary our approach, in which the diameter is a further primitive, enables us to…Read more
  •  1
    TuringL-machines and recursive computability forL-maps
    Studia Logica 48 (2): 179-192. 1989.
    We propose the notion of partial recursiveness and strong partial recursiveness for fuzzy maps. We prove that a fuzzy map f is partial recursive if and only if it is computable by a Turing fuzzy machine and that f is strongly partial recursive and deterministic if and only if it is computable via a deterministic Turing fuzzy machine. This gives a simple and manageable tool to investigate about the properties of the fuzzy machines.
  •  36
    Multivalued Logic to Transform Potential into Actual Objects
    Studia Logica 86 (1): 69-87. 2007.
    We define the notion of “potential existence” by starting from the fact that in multi-valued logic the existential quantifier is interpreted by the least upper bound operator. Besides, we try to define in a general way how to pass from potential into actual existence.
  •  15
    Connection Structures: Grzegorczyk's and Whitehead's Definitions of Point
    with Loredana Biacino
    Notre Dame Journal of Formal Logic 37 (3): 431-439. 1996.
    Whitehead, in his famous book Process and Reality, proposed a definition of point assuming the concepts of "region" and "connection relation" as primitive. Several years after and independently Grzegorczyk, in a brief but very interesting paper, proposed another definition of point in a system in which the inclusion relation and the relation of being separated were assumed as primitive. In this paper we compare their definitions and we show that, under rather natural assumptions, they coincide
  •  20
    Vagueness and Formal Fuzzy Logic: Some Criticisms
    Logic and Logical Philosophy 26 (4). 2017.
  •  44
    Modal logic and model theory
    with Virginia Vaccaro
    Studia Logica 43 (3). 1984.
    We propose a first order modal logic, theQS4E-logic, obtained by adding to the well-known first order modal logicQS4 arigidity axiom schemas:A → □A, whereA denotes a basic formula. In this logic, thepossibility entails the possibility of extending a given classical first order model. This allows us to express some important concepts of classical model theory, such as existential completeness and the state of being infinitely generic, that are not expressibile in classical first order logic. Sinc…Read more
  •  11
    Approximate Similarities and Poincaré Paradox
    Notre Dame Journal of Formal Logic 49 (2): 203-226. 2008.
    De Cock and Kerre, in considering Poincaré paradox, observed that the intuitive notion of "approximate similarity" cannot be adequately represented by the fuzzy equivalence relations. In this note we argue that the deduction apparatus of fuzzy logic gives adequate tools with which to face the question. Indeed, a first-order theory is proposed whose fuzzy models are plausible candidates for the notion of approximate similarity. A connection between these structures and the point-free metric space…Read more
  •  6
    Pavelka's Fuzzy Logic and Free L‐Subsemigroups
    Mathematical Logic Quarterly 31 (7‐8): 123-129. 1985.
  •  14
    Approximate Reasoning Based on Similarity
    with M. Ying and L. Biacino
    Mathematical Logic Quarterly 46 (1): 77-86. 2000.
    The connection between similarity logic and the theory of closure operators is examined. Indeed one proves that the consequence relation defined in [14] can be obtained by composing two closure operators and that the resulting operator is still a closure operator. Also, we extend any similarity into a similarity which is compatible with the logical equivalence, and we prove that this gives the same consequence relation
  • Vaghezza ontologica senza scetticismi
    Rivista di Estetica 49. 2012.
  •  16
    Fuzzy natural deduction
    with Roberto Tortora
    Mathematical Logic Quarterly 36 (1): 67-77. 1990.
  •  19
    Fuzzy logic, continuity and effectiveness
    with Loredana Biacino
    Archive for Mathematical Logic 41 (7): 643-667. 2002.
    It is shown the complete equivalence between the theory of continuous (enumeration) fuzzy closure operators and the theory of (effective) fuzzy deduction systems in Hilbert style. Moreover, it is proven that any truth-functional semantics whose connectives are interpreted in [0,1] by continuous functions is axiomatizable by a fuzzy deduction system (but not by an effective fuzzy deduction system, in general)
  •  4
    Recursively Enumerable L-Sets
    with Loredana Biacino
    Mathematical Logic Quarterly 33 (2): 107-113. 1987.
  •  26
    Fuzzy logic: Mathematical tools for approximate reasoning
    Bulletin of Symbolic Logic 9 (4): 510-511. 2003.
  •  12
    4.4. Il Cervino di Varzi: similarità e oggetti vaghi
    Rivista di Estetica 49 281-296. 2012.
  •  8
    Fuzzy Models of First Order Languages
    with A. di Nola
    Mathematical Logic Quarterly 32 (19‐24): 331-340. 1986.