•  8
    Hybrid Partial Type Theory
    with Antonia Huertas, Patrick Blackburn, Manuel Martins, and Víctor Aranda
    Journal of Symbolic Logic 1-43. forthcoming.
    In this article we define a logical system called Hybrid Partial Type Theory ( $\mathcal {HPTT}$ ). The system is obtained by combining William Farmer’s partial type theory with a strong form of hybrid logic. William Farmer’s system is a version of Church’s theory of types which allows terms to be non-denoting; hybrid logic is a version of modal logic in which it is possible to name worlds and evaluate expressions with respect to particular worlds. We motivate this combination of ideas in the in…Read more
  •  59
    Mario Bunge: A Centenary Festschrift (edited book)
    with Mario Augusto Bunge, Michael R. Matthews, Guillermo M. Denegri, Eduardo L. Ortiz, Heinz W. Droste, Alberto Cordero, Pierre Deleporte, Manuel Crescencio Moreno, Dominique Raynaud, Íñigo Ongay de Felipe, Nicholas Rescher, Richard T. W. Arthur, Rögnvaldur D. Ingthorsson, Evandro Agazzi, Ingvar Johansson, Joseph Agassi, Nimrod Bar-Am, Alberto Cupani, Gustavo E. Romero, Andrés Rivadulla, Art Hobson, Olival Freire Junior, Peter Slezak, Ignacio Morgado-Bernal, Marta Crivos, Leonardo Ivarola, Andreas Pickel, Russell Blackford, Michael Kary, A. Z. Obiedat, Carolina I. García Curilaf, Rafael González del Solar, Luis Marone, Javier Lopez de Casenave, Francisco Yannarella, Mauro A. E. Chaparro, José Geiser Villavicencio- Pulido, Martín Orensanz, Jean-Pierre Marquis, Reinhard Kahle, Ibrahim A. Halloun, José María Gil, Omar Ahmad, Byron Kaldis, Marc Silberstein, Carolina I. García Curilaf, Rafael González del Solar, Javier Lopez de Casenave, Íñigo Ongay de Felipe, and Villavicencio-Pulid
    Springer Verlag. 2019.
    This volume has 41 chapters written to honor the 100th birthday of Mario Bunge. It celebrates the work of this influential Argentine/Canadian physicist and philosopher. Contributions show the value of Bunge’s science-informed philosophy and his systematic approach to philosophical problems. The chapters explore the exceptionally wide spectrum of Bunge’s contributions to: metaphysics, methodology and philosophy of science, philosophy of mathematics, philosophy of physics, philosophy of psychology…Read more
  •  14
    Model Theory
    Oxford University Press. 1990.
    Model theory is the branch of mathematical logic looking at the relationship between mathematical structures and logic languages. These formal languages are free from the ambiguities of natural languages, and are becoming increasingly important in areas such as computing, philosophy and linguistics. This book provides a clear introduction to the subject for both mathematicians and the non-specialists now needing to learn some model theory.
  •  7
    Quantifiers and Conceptual Existence
    with Manuel Crescencio Moreno
    In Mario Augusto Bunge, Michael R. Matthews, Guillermo M. Denegri, Eduardo L. Ortiz, Heinz W. Droste, Alberto Cordero, Pierre Deleporte, María Manzano, Manuel Crescencio Moreno, Dominique Raynaud, Íñigo Ongay de Felipe, Nicholas Rescher, Richard T. W. Arthur, Rögnvaldur D. Ingthorsson, Evandro Agazzi, Ingvar Johansson, Joseph Agassi, Nimrod Bar-Am, Alberto Cupani, Gustavo E. Romero, Andrés Rivadulla, Art Hobson, Olival Freire Junior, Peter Slezak, Ignacio Morgado-Bernal, Marta Crivos, Leonardo Ivarola, Andreas Pickel, Russell Blackford, Michael Kary, A. Z. Obiedat, Carolina I. García Curilaf, Rafael González del Solar, Luis Marone, Javier Lopez de Casenave, Francisco Yannarella, Mauro A. E. Chaparro, José Geiser Villavicencio- Pulido, Martín Orensanz, Jean-Pierre Marquis, Reinhard Kahle, Ibrahim A. Halloun, José María Gil, Omar Ahmad, Byron Kaldis, Marc Silberstein, Carolina I. García Curilaf, Rafael González del Solar, Javier Lopez de Casenave, Íñigo Ongay de Felipe & Villavicencio-Pulid (eds.), Mario Bunge: A Centenary Festschrift, Springer Verlag. pp. 117-138. 2019.
    This chapter examines Bunge’s distinction between the logical concept of existence and the ontological one. We introduce a new conceptual existence predicate in an intensional environment that depends on the evaluation world. So that we can investigate restricted areas where the different kinds of concepts might exist. We hope this new predicate would encompass Bunge’s philosophical position which he designates as conceptualist and fictional materialism. The basic hybridization acts as a bridge …Read more
  •  9
    Identity, equality, nameability and completeness. Part II
    with Manuel Crescencio Moreno
    Bulletin of the Section of Logic 47 (3): 141. 2018.
    This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a notion which has to be defined and, in the other case, identity is a…Read more
  •  27
    Identity, Equality, Nameability and Completeness
    with Manuel Crescencio Moreno
    Bulletin of the Section of Logic 46 (3/4). 2017.
    This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the first is a binary relation between objects while the second is a symbolic relation between terms. Owing to the central role the notion of identity plays in logic, you can be interested either in how to define it using other logical concepts or in the opposite scheme. In the fir…Read more
  •  23
    Completeness in Hybrid Type Theory
    with Carlos Areces, Patrick Blackburn, and Antonia Huertas
    Journal of Philosophical Logic 43 (2-3): 209-238. 2014.
    We show that basic hybridization makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin…Read more
  •  53
    Formalización en teoría de tipos del predicado de existencia de Mario Bunge
    Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 1 (2): 513-534. 1985.
    Professor Bunge makes the distinction between the logical concept of existence and the ontological one. I agree with him and in this paper I am formalizing his existence predicate into the powerful language of type theory.I am also proving the logical equivalence of this for mulation with a briefer one, which says that to exist conceptually is the same as to be a conceptual object. Accordingly, from this point on I investigate what conceptual objects are. I reach the conclusion that it is better…Read more
  •  43
    Diagonalisation and Church's Thesis: Kleene's Homework
    with Enrique Alonso
    History and Philosophy of Logic 26 (2): 93-113. 2005.
    In this paper we will discuss the active part played by certain diagonal arguments in the genesis of computability theory. 1 In some cases it is enough to assume the enumerability of Y while in others the effective enumerability is a substantial demand. These enigmatical words by Kleene were our point of departure: When Church proposed this thesis, I sat down to disprove it by diagonalizing out of the class of the λ–definable functions. But, quickly realizing that the diagonalization cannot be d…Read more
  •  5
    Modelos, teoría de
    In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica, Editorial Trotta. pp. 410--413. 2011.
  •  116
    Completeness in Hybrid Type Theory
    with Carlos Areces, Patrick Blackburn, and Antonia Huertas
    Journal of Philosophical Logic (2-3): 1-30. 2013.
    We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret $@_i$ in propositional and first-order hybrid logic. This means: interpret $@_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of type $a$ that rigid…Read more
  •  22
    Editorial ‘Tools for Teaching Logic’
    Logic Journal of the IGPL 15 (4): 289-292. 2007.
  •  22
    A note on Visions of Henkin
    with Enrique Alonso
    Synthese 194 (6): 1839-1840. 2017.
  •  10
    The 1st Barcelona Symposium on History and Philosophy of Science
    Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 2 (2-3): 645-646. 1987.
  •  79
    Hybrid Type Theory: A Quartet in Four Movements
    with Carlos Areces, Patrick Blackburn, and Antonia Huertas
    Principia: An International Journal of Epistemology 15 (2): 225. 2011.
    Este artigo canta uma canção — uma canção criada ao unir o trabalho de quatro grandes nomes na história da lógica: Hans Reichenbach, Arthur Prior, Richard Montague, e Leon Henkin. Embora a obra dos primeiros três desses autores tenha sido previamente combinada, acrescentar as ideias de Leon Henkin é o acréscimo requerido para fazer com que essa combinação funcione no nível lógico. Mas o presente trabalho não se concentra nas tecnicalidades subjacentes (que podem ser encontradas em Areces, Blackb…Read more
  •  70
    Completeness: from Gödel to Henkin
    with Enrique Alonso
    History and Philosophy of Logic 35 (1): 1-26. 2014.
    This paper focuses on the evolution of the notion of completeness in contemporary logic. We discuss the differences between the notions of completeness of a theory, the completeness of a calculus, and the completeness of a logic in the light of Gödel's and Tarski's crucial contributions.We place special emphasis on understanding the differences in how these concepts were used then and now, as well as on the role they play in logic. Nevertheless, we can still observe a certain ambiguity in the us…Read more
  •  44
    Visions of Henkin
    with Enrique Alonso
    Synthese 192 (7): 2123-2138. 2015.
    Leon Henkin (1921–2006) was not only an extraordinary logician, but also an excellent teacher, a dedicated professor and an exceptional person. The first two sections of this paper are biographical, discussing both his personal and academic life. In the last section we present three aspects of Henkin’s work. First we comment part of his work fruit of his emphasis on teaching. In a personal communication he affirms that On mathematical induction, published in 1969, was the favourite among his art…Read more
  •  12
    Hybrid Type Theory: A Quartet in Four Movements DOI:10.5007/1808-1711.2011v15n2p225
    with Carlos Areces, Patrick Blackburn, and Antonia Huertas
    Principia: An International Journal of Epistemology 15 (2): 225-247. 2011.
    This paper sings a song — a song created by bringing together the work of four great names in the history of logic: Hans Reichenbach, Arthur Prior, Richard Montague, and Leon Henkin. Although the work of the first three of these authors have previously been combined, adding the ideas of Leon Henkin is the addition required to make the combination work at the logical level. But the present paper does not focus on the underlying technicalities rather it focusses on the underlying instruments, and …Read more
  •  99
    Extensions of first order logic
    Cambridge University Press. 1996.
    Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing …Read more
  • Vida, obra y algunos milagros de Alonzo Church
    Agora 18 (1): 107-132. 1999.