41 found
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  1. Giangiacomo Gerla & Bonaventura Paolillo (2010). Whitehead's Pointfree Geometry and Diametric Posets. Logic and Logical Philosophy 19 (4):289-308.
    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 avoid (...)
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  2.  16
    Loredana Biacino & Giangiacomo Gerla (1991). Connection Structures. Notre Dame Journal of Formal Logic 32 (2):242-247.
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  3.  24
    Giangiacomo Gerla (2003). Fuzzy Logic: Mathematical Tools for Approximate Reasoning. Bulletin of Symbolic Logic 9 (4):510-511.
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  4.  26
    Giangiacomo Gerla (1992). Distances, Diameters and Verisimilitude of Theories. Archive for Mathematical Logic 31 (6):407-414.
  5. Giangiacomo Gerla (2007). Point-Free Geometry and Verisimilitude of Theories. Journal of Philosophical Logic 36 (6):707 - 733.
    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. This avoids some of the difficulties (...)
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  6.  12
    Ferrante Formato & Giangiacomo Gerla (1998). Grasping Infinity by Finite Sets. Mathematical Logic Quarterly 44 (3):383-393.
    We show that the existence of an infinite set can be reduced to the existence of finite sets “as big as we will”, provided that a multivalued extension of the relation of equipotence is admitted. In accordance, we modelize the notion of infinite set by a fuzzy subset representing the class of wide sets.
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  7.  3
    Loredana Biacino & Giangiacomo Gerla (2002). Fuzzy Logic, Continuity and Effectiveness. Archive for Mathematical Logic 41 (7):643-667.
    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).
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  8.  30
    Giangiacomo Gerla (2005). Fuzzy Logic Programming and Fuzzy Control. Studia Logica 79 (2):231 - 254.
    We show that it is possible to base fuzzy control on fuzzy logic programming. Indeed, we observe that the class of fuzzy Herbrand interpretations gives a semantics for fuzzy programs and we show that the fuzzy function associated with a fuzzy system of IF-THEN rules is the fuzzy Herbrand interpretation associated with a suitable fuzzy program.
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  9.  16
    Giangiacomo Gerla (1990). Pointless Metric Spaces. Journal of Symbolic Logic 55 (1):207-219.
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  10.  5
    Giangiacomo Gerla (1987). Decidability, Partial Decidability and Sharpness Relation for L-Subsets. Studia Logica 46 (3):227-238.
    If X is set and L a lattice, then an L-subset or fuzzy subset of X is any map from X to L, [11]. In this paper we extend some notions of recursivity theory to fuzzy set theory, in particular we define and examine the concept of almost decidability for L-subsets. Moreover, we examine the relationship between imprecision and decidability. Namely, we prove that there exist infinitely indeterminate L-subsets with no more precise decidable versions and classical subsets whose unique shaded (...)
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  11.  4
    Loredana Biacino & Giangiacomo Gerla (1996). Connection Structures: Grzegorczyk's and Whitehead's Definitions of Point. Notre Dame Journal of Formal Logic 37 (3):431-439.
    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.
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  12.  12
    Giangiacomo Gerla (1989). Turing L -Machines and Recursive Computability for L -Maps. Studia Logica 48 (2):179 - 192.
    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.
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  13.  29
    Cristina Coppola, Giangiacomo Gerla & Annamaria Miranda (2010). Point-Free Foundation of Geometry and Multivalued Logic. Notre Dame Journal of Formal Logic 51 (3):383-405.
    Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach , whose primitive notions are regions and inclusion relation between regions, and the connection-based approach , where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.
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  14.  10
    Cristina Coppola & Giangiacomo Gerla (2013). Special Issue on Point-Free Geometry and Topology. Logic and Logical Philosophy 22 (2):139-143.
    In the first section we briefly describe methodological assumptions of point-free geometry and topology. We also outline history of geometrical theories based on the notion of emph{region}. The second section is devoted to concise presentation of the content of the LLP special issue on point-free theories of space.
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  15. Loredana Biacino & Giangiacomo Gerla (1987). Recursively Enumerable L‐Sets. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (2):107-113.
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  16.  1
    Giangiacomo Gerla (1994). An Extension Principle for Fuzzy Logics. Mathematical Logic Quarterly 40 (3):357-380.
    Let S be a set, P the class of all subsets of S and F the class of all fuzzy subsets of S. In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined in P into a fuzzy closure operator J* defined in F. This enables us to give the notion of canonical extension of a deduction system and to (...)
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  17.  2
    Loredana Biacino & Giangiacomo Gerla (1989). Decidability, Recursive Enumerability and Kleene Hierarchy For L‐Subsets. Mathematical Logic Quarterly 35 (1):49-62.
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  18.  20
    Giangiacomo Gerla & Virginia Vaccaro (1984). Modal Logic and Model Theory. Studia Logica 43 (3):203 - 216.
    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. Since they can be expressed in (...)
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  19. Giangiacomo Gerla (1987). Transformational Semantics for First Order Logic. Logique Et Analyse 117 (17):118.
     
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  20.  12
    Giangiacomo Gerla (2006). Effectiveness and Multivalued Logics. Journal of Symbolic Logic 71 (1):137 - 162.
    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.
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  21.  1
    Giangiacomo Gerla (2012). 4.4. Il Cervino di Varzi: similarita e oggetti vaghi. Rivista di Estetica 52 (49):281-296.
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  22.  3
    Giangiacomo Gerla (1985). Pavelka's Fuzzy Logic and Free L‐Subsemigroups. Mathematical Logic Quarterly 31 (7‐8):123-129.
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  23.  9
    Giangiacomo Gerla (2007). Multivalued Logic to Transform Potential Into Actual Objects. Studia Logica 86 (1):69 - 87.
    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.
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  24.  1
    Giangiacomo Gerla & Roberto Tortora (1990). Fuzzy Natural Deduction. Mathematical Logic Quarterly 36 (1):67-77.
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  25.  1
    Giangiacomo Gerla (1996). Graded Consequence Relations and Fuzzy Closure Operator. Journal of Applied Non-Classical Logics 6 (4):369-379.
    ABSTRACT In this work the connections between the fuzzy closure operators and the graded consequence relations are examined Namely, as it is well known, in the crisp case there is a complete equivalence between the notion of closure operator and the one of consequence relation. We extend this result by proving that the graded consequence relations are related to a particular class of fuzzy closure operators, namely the class of fuzzy closure operators that can be obtained by a chain of (...)
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  26.  1
    Daniele Genito & Giangiacomo Gerla (2013). Connecting Bilattice Theory with Multivalued Logic. Logic and Logical Philosophy 23 (1):15-45.
    This is an exploratory paper whose aim is to investigate the potentialities of bilattice theory for an adequate definition of the deduction apparatus for multi-valued logic. We argue that bilattice theory enables us to obtain a nice extension of the graded approach to fuzzy logic. To give an example, a completeness theorem for a logic based on Boolean algebras is proved.
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  27.  1
    Giangiacomo Gerla (1982). A Note on the Principle of Predication. Notre Dame Journal of Formal Logic 23 (4):471-472.
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  28. Loredana Biacino & Giangiacomo Gerla (1989). Decidability, Recursive Enumerability and Kleene Hierarchy ForL-Subsets. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (1):49-62.
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  29. Giangiacomo Gerla (2012). Cervino of the Varzi: Similarity and Vague Objects. Rivista di Estetica 52 (1):281-296.
     
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  30. Giangiacomo Gerla & Roberto Tortora (1996). Dissezioni e intersezioni di regioni in AN Whitehead. Epistemologia 19 (2):289-308.
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  31. Giangiacomo Gerla (2005). Fuzzy Logic Programming and Fuzzy Control. Studia Logica 79 (2):231-254.
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  32. Giangiacomo Gerla & Roberto Tortora (1990). Fuzzy Natural Deduction. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (1):67-77.
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  33. Giangiacomo Gerla & Roberto Tortora (1992). La relazione di connessione in AN Whitehead: Aspetti matematici. Epistemologia 15 (2):351-364.
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  34. Giangiacomo Gerla (2007). Multivalued Logic to Transform Potential Into Actual Objects. Studia Logica 86 (1):69-87.
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  35. Giangiacomo Gerla (1989). On the Logical Structure of Verisimilitude. Epistemologia 12 (1):161.
     
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  36. Giangiacomo Gerla (1985). Pavelka's Fuzzy Logic and Free L-Subsemigroups. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (7-8):123-129.
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  37. Giangiacomo Gerla (2007). Point-Free Geometry and Verisimilitude of Theories. Journal of Philosophical Logic 36 (6):707-733.
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  38. Giangiacomo Gerla (1989). TuringL-Machines and Recursive Computability forL-Maps. Studia Logica 48 (2):179-192.
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  39. Giangiacomo Gerla (2012). Vaghezza ontologica senza scetticismi. Rivista di Estetica 52 (1).
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  40. Giangiacomo Gerla (2008). Approximate Similarities and Poincaré Paradox. Notre Dame Journal of Formal Logic 49 (2):203-226.
    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 spaces is also established.
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  41. Annamaria Miranda & Giangiacomo Gerla (2008). Mathematical Features of Whitehead’s Point-Free Geometry. In Michel Weber (ed.), Handbook of Whiteheadian Process Thought. De Gruyter 119-130.
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