Switch to: References

Add citations

You must login to add citations.
  1. Eligibility and Inscrutability.J. Robert G. Williams - 2007 - Philosophical Review 116 (3):361-399.
    Inscrutability arguments threaten to reduce interpretationist metasemantic theories to absurdity. Can we find some way to block the arguments? A highly influential proposal in this regard is David Lewis’ ‘ eligibility ’ response: some theories are better than others, not because they fit the data better, but because they are framed in terms of more natural properties. The purposes of this paper are to outline the nature of the eligibility proposal, making the case that it is not ad hoc, but (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   71 citations  
  • Completeness and Categoricity. Part I: Nineteenth-Century Axiomatics to Twentieth-Century Metalogic.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (1):1-30.
    This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   36 citations  
  • Higher-Order Aspects and Context in SUMO.Christoph Benzmüller & Adam Pease - 2012 - Journal of Web Semantics 12:104-117.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  • Sweet SIXTEEN: Automation Via Embedding Into Classical Higher-Order Logic.Alexander Steen & Christoph Benzmüller - 2016 - Logic and Logical Philosophy 25 (4):535-554.
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  • The Semantic View of Theories and Higher-Order Languages.Laurenz Hudetz - 2019 - Synthese 196 (3):1131-1149.
    Several philosophers of science construe models of scientific theories as set-theoretic structures. Some of them moreover claim that models should not be construed as structures in the sense of model theory because the latter are language-dependent. I argue that if we are ready to construe models as set-theoretic structures, we could equally well construe them as model-theoretic structures of higher-order logic. I show that every family of set-theoretic structures has an associated language of higher-order logic and an up to signature (...)
    No categories
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  • Lesniewski and Russell's Paradox: Some Problems.Rafal Urbaniak - 2008 - History and Philosophy of Logic 29 (2):115-146.
    Sobocinski in his paper on Leśniewski's solution to Russell's paradox (1949b) argued that Leśniewski has succeeded in explaining it away. The general strategy of this alleged explanation is presented. The key element of this attempt is the distinction between the collective (mereological) and the distributive (set-theoretic) understanding of the set. The mereological part of the solution, although correct, is likely to fall short of providing foundations of mathematics. I argue that the remaining part of the solution which suggests a specific (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Russell's 1925 Logic.A. P. Hazen & J. M. Davoren - 2000 - Australasian Journal of Philosophy 78 (4):534 – 556.
  • Domains of Sciences, Universes of Discourse and Omega Arguments.Jose M. Saguillo - 1999 - History and Philosophy of Logic 20 (3-4):267-290.
    Each science has its own domain of investigation, but one and the same science can be formalized in different languages with different universes of discourse. The concept of the domain of a science and the concept of the universe of discourse of a formalization of a science are distinct, although they often coincide in extension. In order to analyse the presuppositions and implications of choices of domain and universe, this article discusses the treatment of omega arguments in three very different (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  • Alonzo Church:His Life, His Work and Some of His Miracles.Maía Manzano - 1997 - History and Philosophy of Logic 18 (4):211-232.
    This paper is dedicated to Alonzo Church, who died in August 1995 after a long life devoted to logic. To Church we owe lambda calculus, the thesis bearing his name and the solution to the Entscheidungsproblem.His well-known book Introduction to Mathematical LogicI, defined the subject matter of mathematical logic, the approach to be taken and the basic topics addressed. Church was the creator of the Journal of Symbolic Logicthe best-known journal of the area, which he edited for several decades This (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • Discussions on Physics, Metaphysics and Metametaphysics: Interpreting Quantum Mechanics.Raoni Wohnrath Arroyo - 2020 - Dissertation, Federal University of Santa Catarina
    This thesis inquires what it means to interpret non-relativistic quantum mechanics (QM), and the philosophical limits of this interpretation. In pursuit of a scientific-realist stance, a metametaphysical method is expanded and applied to evaluate rival interpretations of QM, based on the conceptual distinction between ontology and metaphysics, for objective theory choice in metaphysical discussions relating to QM. Three cases are examined, in which this metametaphysical method succeeds in indicating what are the wrong alternatives to interpret QM in metaphysical terms. The (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • To Be F Is To Be G.Cian Dorr - 2016 - Philosophical Perspectives 30 (1):39-134.
    This paper is an investigation of the general logic of "identifications", claims such as 'To be a vixen is to be a female fox', 'To be human is to be a rational animal', and 'To be just is to help one's friends and harm one's enemies', many of which are of great importance to philosophers. I advocate understanding such claims as expressing higher-order identity, and discuss a variety of different general laws which they might be thought to obey. [New version: (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   90 citations  
  • Cumulative Habilitation Script.Christoph Benzmüller - 2006 - Saarland University, Germany.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  • Tracing Internal Categoricity.Jouko Väänänen - 2021 - Theoria 87 (4):986-1000.
    No categories
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Type-Logical Semantics.Reinhard Muskens - 2011 - Routledge Encyclopedia of Philosophy Online.
    Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  • Choice and Descriptions in Enriched Intensional Languages — I.R. Routley, R. K. Meyer & L. Goddard - 1974 - Journal of Philosophical Logic 3 (3):291 - 316.
  • Universal Semantics?Richard Routley - 1975 - Journal of Philosophical Logic 4 (3):327 - 356.
  • Dunn's Relevant Predication, Real Properties and Identity.Philip Kremer - 1997 - Erkenntnis 47 (1):37-65.
    We critically investigate and refine Dunn's relevant predication, his formalisation of the notion of a real property. We argue that Dunn's original dialectical moves presuppose some interpretation of relevant identity, though none is given. We then re-motivate the proposal in a broader context, considering the prospects for a classical formalisation of real properties, particularly of Geach's implicit distinction between real and ''Cambridge'' properties. After arguing against these prospects, we turn to relevance logic, re-motivating relevant predication with Geach's distinction in mind. (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  • Strict Coherence, Sigma Coherence and the Metaphysics of Quantity.Brian Skyrms - 1995 - Philosophical Studies 77 (1):39-55.
  • First-Order Definability of Transition Structures.Antje Rumberg & Alberto Zanardo - 2019 - Journal of Logic, Language and Information 28 (3):459-488.
    The transition semantics presented in Rumberg (J Log Lang Inf 25(1):77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language L_t are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves L_t-validity w.r.t. transition structures. As a consequence, for a certain fragment of L_t, validity (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Pecularities of Some Three- and Four-Valued Second Order Logics.Allen P. Hazen & Francis Jeffry Pelletier - 2018 - Logica Universalis 12 (3-4):493-509.
    Logics that have many truth values—more than just True and False—have been argued to be useful in the analysis of very many philosophical and linguistic puzzles. In this paper, which is a followup to, we will start with a particularly well-motivated four-valued logic that has been studied mainly in its propositional and first-order versions. And we will then investigate its second-order version. This four-valued logic has two natural three-valued extensions: what is called a “gap logic”, and what is called a (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • The Broadest Necessity.Andrew Bacon - 2018 - Journal of Philosophical Logic 47 (5):733-783.
    In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   17 citations  
  • Cut-Elimination for Quantified Conditional Logic.Christoph Benzmüller - 2017 - Journal of Philosophical Logic 46 (3):333-353.
    A semantic embedding of quantified conditional logic in classical higher-order logic is utilized for reducing cut-elimination in the former logic to existing results for the latter logic. The presented embedding approach is adaptable to a wide range of other logics, for many of which cut-elimination is still open. However, special attention has to be payed to cut-simulation, which may render cut-elimination as a pointless criterion.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Completeness and Decidability of General First-Order Logic.Aldo Antonelli - 2017 - Journal of Philosophical Logic 46 (3):233-257.
    This paper investigates the “general” semantics for first-order logic introduced to Antonelli, 637–58, 2013): a sound and complete axiom system is given, and the satisfiability problem for the general semantics is reduced to the satisfiability of formulas in the Guarded Fragment of Andréka et al. :217–274, 1998), thereby showing the former decidable. A truth-tree method is presented in the Appendix.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Comparing Approaches To Resolution Based Higher-Order Theorem Proving.Christoph Benzmüller - 2002 - Synthese 133 (1):203-335.
    We investigate several approaches to resolution based automated theoremproving in classical higher-order logic (based on Church's simply typed-calculus) and discuss their requirements with respect to Henkincompleteness and full extensionality. In particular we focus on Andrews'higher-order resolution (Andrews 1971), Huet's constrained resolution (Huet1972), higher-order E-resolution, and extensional higher-order resolution(Benzmüller and Kohlhase 1997). With the help of examples we illustratethe parallels and differences of the extensionality treatment of these approachesand demonstrate that extensional higher-order resolution is the sole approach thatcan completely avoid additional (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • A Note on Carnap's Meaning Criterion.William W. Rozeboom - 1960 - Philosophical Studies 11 (3):33 - 38.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • A 'Natural Logic' Inference System Using the Lambek Calculus.Anna Zamansky, Nissim Francez & Yoad Winter - 2006 - Journal of Logic, Language and Information 15 (3):273-295.
    This paper develops an inference system for natural language within the ‘Natural Logic’ paradigm as advocated by van Benthem, Sánchez and others. The system that we propose is based on the Lambek calculus and works directly on the Curry-Howard counterparts for syntactic representations of natural language, with no intermediate translation to logical formulae. The Lambek -based system we propose extends the system by Fyodorov et~al., which is based on the Ajdukiewicz/Bar-Hillel calculus Bar Hillel,. This enables the system to deal with (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  • A Higher-Order Theory of Presupposition.Scott Martin & Carl Pollard - 2012 - Studia Logica 100 (4):727-751.
    So-called 'dynamic' semantic theories such as Kamp's discourse representation theory and Heim's file change semantics account for such phenomena as cross-sentential anaphora, donkey anaphora, and the novelty condition on indefinites, but compare unfavorably with Montague semantics in some important respects (clarity and simplicity of mathematical foundations, compositionality, handling of quantification and coordination). Preliminary efforts have been made by Muskens and by de Groote to revise and extend Montague semantics to cover dynamic phenomena. We present a new higher-order theory of discourse (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  • Completeness in Hybrid Type Theory.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2013 - Journal of Philosophical Logic (2-3):1-30.
    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 [email protected]_i$ in propositional and first-order hybrid logic. This means: interpret [email protected]_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of type $a$ that (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  • Forcing, Downward Löwenheim-Skolem and Omitting Types Theorems, Institutionally.Daniel Găină - 2014 - Logica Universalis 8 (3-4):469-498.
    In the context of proliferation of many logical systems in the area of mathematical logic and computer science, we present a generalization of forcing in institution-independent model theory which is used to prove two abstract results: Downward Löwenheim-Skolem Theorem and Omitting Types Theorem . We instantiate these general results to many first-order logics, which are, roughly speaking, logics whose sentences can be constructed from atomic formulas by means of Boolean connectives and classical first-order quantifiers. These include first-order logic , logic (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  • The Metaphysics of Quantity.Brent Mundy - 1987 - Philosophical Studies 51 (1):29 - 54.
    A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically second-order (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically first-order (while logically non-elementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing first-order theories of quantity in that it does not depend upon empirically (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   61 citations  
  • Matters of Relevance.Hugues Leblanc - 1972 - Journal of Philosophical Logic 1 (3/4):269 - 286.
  • The Three Arrows of Zeno.Craig Harrison - 1996 - Synthese 107 (2):271 - 292.
    We explore the better known paradoxes of Zeno including modern variants based on infinite processes, from the point of view of standard, classical analysis, from which there is still much to learn (especially concerning the paradox of division), and then from the viewpoints of non-standard and non-classical analysis (the logic of the latter being intuitionist).The standard, classical or Cantorian notion of the continuum, modeled on the real number line, is well known, as is the definition of motion as the time (...)
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  • Elementary Categorial Logic, Predicates of Variable Degree, and Theory of Quantity.Brent Mundy - 1989 - Journal of Philosophical Logic 18 (2):115 - 140.
    Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. This (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  • Frege's Double Correlation Thesis and Quine's Set Theories NF and ML.Nino B. Cocchiarella - 1985 - Journal of Philosophical Logic 14 (1):1 - 39.
  • Consistency and Konsistenz.William Boos - 1987 - Erkenntnis 26 (1):1 - 43.
    A ground-motive for this study of some historical and metaphysical implications of the diagonal lemmas of Cantor and Gödel is Cantor's insightful remark to Dedekind in 1899 that the Inbegriff alles Denkbaren (aggregate of everything thinkable) might, like some class-theoretic entities, be inkonsistent. In the essay's opening sections, I trace some recent antecedents of Cantor's observation in logical writings of Bolzano and Dedekind (more remote counterparts of his language appear in the First Critique), then attempt to relativize the notion of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Critical Notice.J. F. A. K. Benthem - 1979 - Synthese 40 (2):353-373.
    Gabbay has gathered an enormous amount of results; some of them important and novel, others important but already known, many rather routine, however. The organization of this material shows grave defects, both in the exposition and in its logical structure. Intensional logic appears as a vast collection of (often duplicated) loosely connected results. This may be a true reflection of the present state of the subject, but it does not contribute to a better understanding of it, let alone advance it.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  • Carnap's Work in the Foundations of Logic and Mathematics in a Historical Perspective.Jaakko Hintikka - 1992 - Synthese 93 (1-2):167 - 189.
    Carnap's philosophy is examined from new viewpoints, including three important distinctions: (i) language as calculus vs language as universal medium; (ii) different senses of completeness: (iii) standard vs nonstandard interpretations of (higher-order) logic. (i) Carnap favored in 1930-34 the "formal mode of speech," a corollary to the universality assumption. He later gave it up partially but retained some of its ingredients, e.g., the one-domain assumption. (ii) Carnap's project of creating a universal self-referential language is encouraged by (ii) and by the (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  • Is “Some-Other-Time” Sometimes Better Than “Sometime” for Proving Partial Correctness of Programs?Ildikó Sain - 1988 - Studia Logica 47 (3):279 - 301.
    The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal logic increases the (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Limits of Inquiry.William Boos - 1983 - Erkenntnis 20 (2):157 - 194.
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • A Relational Formulation of the Theory of Types.Reinhard Muskens - 1989 - Linguistics and Philosophy 12 (3):325 - 346.
    This paper developes a relational---as opposed to a functional---theory of types. The theory is based on Hilbert and Bernays' eta operator plus the identity symbol, from which Church's lambda and the other usual operators are then defined. The logic is intended for use in the semantics of natural language.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • Dynamic Squares.Patrick Blackburn & Yde Venema - 1995 - Journal of Philosophical Logic 24 (5):469 - 523.
  • Logica Universalis: Towards a General Theory of Logic.Jean-Yves Béziau (ed.) - 2007 - Birkhäuser Basel.
    Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last (...)
    Direct download (4 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  • Second-Order Logic of Paradox.Allen P. Hazen & Francis Jeffry Pelletier - 2018 - Notre Dame Journal of Formal Logic 59 (4):547-558.
    The logic of paradox, LP, is a first-order, three-valued logic that has been advocated by Graham Priest as an appropriate way to represent the possibility of acceptable contradictory statements. Second-order LP is that logic augmented with quantification over predicates. As with classical second-order logic, there are different ways to give the semantic interpretation of sentences of the logic. The different ways give rise to different logical advantages and disadvantages, and we canvass several of these, concluding that it will be extremely (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • General Models and Entailment Semantics for Independence Logic.Pietro Galliani - 2013 - Notre Dame Journal of Formal Logic 54 (2):253-275.
    We develop a semantics for independence logic with respect to what we will call general models. We then introduce a simpler entailment semantics for the same logic, and we reduce the validity problem in the former to the validity problem in the latter. Then we build a proof system for independence logic and prove its soundness and completeness with respect to entailment semantics.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • Skolem Redux.W. D. Hart - 2000 - Notre Dame Journal of Formal Logic 41 (4):399--414.
    Hume's Principle requires the existence of the finite cardinals and their cardinal, but these are the only cardinals the Principle requires. Were the Principle an analysis of the concept of cardinal number, it would already be peculiar that it requires the existence of any cardinals; an analysis of bachelor is not expected to yield unmarried men. But that it requires the existence of some cardinals, the countable ones, but not others, the uncountable, makes it seem invidious; it is as if (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  • Internal Categoricity in Arithmetic and Set Theory.Jouko Väänänen & Tong Wang - 2015 - Notre Dame Journal of Formal Logic 56 (1):121-134.
    We show that the categoricity of second-order Peano axioms can be proved from the comprehension axioms. We also show that the categoricity of second-order Zermelo–Fraenkel axioms, given the order type of the ordinals, can be proved from the comprehension axioms. Thus these well-known categoricity results do not need the so-called “full” second-order logic, the Henkin second-order logic is enough. We also address the question of “consistency” of these axiom systems in the second-order sense, that is, the question of existence of (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  • Propositional Quantification in the Topological Semantics for S.Philip Kremer - 1997 - Notre Dame Journal of Formal Logic 38 (2):295-313.
    Fine and Kripke extended S5, S4, S4.2 and such to produce propositionally quantified systems , , : given a Kripke frame, the quantifiers range over all the sets of possible worlds. is decidable and, as Fine and Kripke showed, many of the other systems are recursively isomorphic to second-order logic. In the present paper I consider the propositionally quantified system that arises from the topological semantics for S4, rather than from the Kripke semantics. The topological system, which I dub , (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • Reduction and Tarski's Definition of Logical Consequence.Jim Edwards - 2003 - Notre Dame Journal of Formal Logic 44 (1):49-62.
    In his classic 1936 paper Tarski sought to motivate his definition of logical consequence by appeal to the inference form: P(0), P(1), . . ., P(n), . . . therefore ∀nP(n). This is prima facie puzzling because these inferences are seemingly first-order and Tarski knew that Gödel had shown first-order proof methods to be complete, and because ∀nP(n) is not a logical consequence of P(0), P(1), . . ., P(n), . . . by Taski's proposed definition. An attempt to resolve (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Boolean-Valued Second-Order Logic.Daisuke Ikegami & Jouko Väänänen - 2015 - Notre Dame Journal of Formal Logic 56 (1):167-190.
    In so-called full second-order logic, the second-order variables range over all subsets and relations of the domain in question. In so-called Henkin second-order logic, every model is endowed with a set of subsets and relations which will serve as the range of the second-order variables. In our Boolean-valued second-order logic, the second-order variables range over all Boolean-valued subsets and relations on the domain. We show that under large cardinal assumptions Boolean-valued second-order logic is more robust than full second-order logic. Its (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Syntax and Semantics of the Logic $\mathcal{L}^\lambda_{\omega\omega}$.Carsten Butz - 1997 - Notre Dame Journal of Formal Logic 38 (3):374-384.
    In this paper we study the logic $\mathcal{L}^\lambda_{\omega\omega}$, which is first-order logic extended by quantification over functions . We give the syntax of the logic as well as the semantics in Heyting categories with exponentials. Embedding the generic model of a theory into a Grothendieck topos yields completeness of $\mathcal{L}^\lambda_{\omega\omega}$ with respect to models in Grothendieck toposes, which can be sharpened to completeness with respect to Heyting-valued models. The logic $\mathcal{L}^\lambda_{\omega\omega}$ is the strongest for which Heyting-valued completeness is known. Finally, (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark