61 found
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  1. Albert Visser & Ali Enayat (2015). New Constructions of Satisfaction Classes. In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Netherlands
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  2.  7
    Albert Visser (2009). The Predicative Frege Hierarchy. Annals of Pure and Applied Logic 160 (2):129-153.
    In this paper, we characterize the strength of the predicative Frege hierarchy, , introduced by John Burgess in his book [J. Burgess, Fixing frege, in: Princeton Monographs in Philosophy, Princeton University Press, Princeton, 2005]. We show that and are mutually interpretable. It follows that is mutually interpretable with Q. This fact was proved earlier by Mihai Ganea in [M. Ganea, Burgess’ PV is Robinson’s Q, The Journal of Symbolic Logic 72 619–624] using a different proof. Another consequence of the our (...)
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  3.  12
    Albert Visser (2008). Pairs, Sets and Sequences in First-Order Theories. Archive for Mathematical Logic 47 (4):299-326.
    In this paper we study the idea of theories with containers, like sets, pairs, sequences. We provide a modest framework to study such theories. We prove two concrete results. First, we show that first-order theories of finite signature that have functional non-surjective ordered pairing are definitionally equivalent to extensions in the same language of the basic theory of non-surjective ordered pairing. Second, we show that a first-order theory of finite signature is sequential (is a theory of sequences) iff it is (...)
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  4.  18
    Albert Visser (2012). The Second Incompleteness Theorem and Bounded Interpretations. Studia Logica 100 (1-2):399-418.
    In this paper we formulate a version of Second Incompleteness Theorem. The idea is that a sequential sentence has ‘consistency power’ over a theory if it enables us to construct a bounded interpretation of that theory. An interpretation of V in U is bounded if, for some n , all translations of V -sentences are U -provably equivalent to sentences of complexity less than n . We call a sequential sentence with consistency power over T a pro-consistency statement for T (...)
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  5.  13
    Albert Visser (2016). Transductions in Arithmetic. Annals of Pure and Applied Logic 167 (3):211-234.
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  6.  15
    Clemens Grabmayer, Joop Leo, Vincent van Oostrom & Albert Visser (2011). On the Termination of Russell's Description Elimination Algorithm. Review of Symbolic Logic 4 (3):367-393.
    In this paper we study the termination behavior of Russell’s description elimination rewrite system. We discuss certain claims made by Kripke (2005) in his paper concerning the possible nontermination of elimination of descriptions.
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  7.  7
    Albert Visser (2005). Faith & Falsity. Annals of Pure and Applied Logic 131 (1):103-131.
    A theory T is trustworthy iff, whenever a theory U is interpretable in T, then it is faithfully interpretable. In this paper we give a characterization of trustworthiness. We provide a simple proof of Friedman’s Theorem that finitely axiomatized, sequential, consistent theories are trustworthy. We provide an example of a theory whose schematic predicate logic is complete Π20.
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  8.  7
    Albert Visser (2009). Growing Commas. A Study of Sequentiality and Concatenation. Notre Dame Journal of Formal Logic 50 (1):61-85.
    In his paper "Undecidability without arithmetization," Andrzej Grzegorczyk introduces a theory of concatenation $\mathsf{TC}$. We show that pairing is not definable in $\mathsf{TC}$. We determine a reasonable extension of $\mathsf{TC}$ that is sequential, that is, has a good sequence coding.
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  9.  24
    Albert Visser (1989). Semantics and the Liar Paradox. Handbook of Philosophical Logic 4 (1):617--706.
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  10.  45
    Albert Visser (1984). Four Valued Semantics and the Liar. Journal of Philosophical Logic 13 (2):181 - 212.
  11.  14
    Albert Visser (2012). Vaught's Theorem on Axiomatizability by a Scheme. Bulletin of Symbolic Logic 18 (3):382-402.
    In his 1967 paper Vaught used an ingenious argument to show that every recursively enumerable first order theory that directly interprets the weak system VS of set theory is axiomatizable by a scheme. In this paper we establish a strengthening of Vaught's theorem by weakening the hypothesis of direct interpretability of VS to direct interpretability of the finitely axiomatized fragment VS2 of VS. This improvement significantly increases the scope of the original result, since VS is essentially undecidable, but VS2 has (...)
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  12.  45
    Albert Visser (1981). A Propositional Logic with Explicit Fixed Points. Studia Logica 40 (2):155 - 175.
    This paper studies a propositional logic which is obtained by interpreting implication as formal provability. It is also the logic of finite irreflexive Kripke Models.A Kripke Model completeness theorem is given and several completeness theorems for interpretations into Provability Logic and Peano Arithmetic.
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  13.  35
    Albert Visser (1991). The Formalization of Interpretability. Studia Logica 50 (1):81 - 105.
    This paper contains a careful derivation of principles of Interpretability Logic valid in extensions of I0+1.
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  14.  10
    Volker Halbach & Albert Visser (2014). Self-Reference in Arithmetic I. Review of Symbolic Logic 7 (4):671-691.
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  15.  3
    Albert Visser (1993). The Unprovability of Small Inconsistency. Archive for Mathematical Logic 32 (4):275-298.
    We show that a consistent, finitely axiomatized, sequential theory cannot prove its own inconsistency on every definable cut. A corollary is that there are at least three degrees of global interpretability of theories equivalent modulo local interpretability to a consistent, finitely axiomatized, sequential theory U.
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  16.  6
    Albert Visser & Maartje de Jonge (2006). No Escape From Vardanyan's Theorem. Archive for Mathematical Logic 45 (5):539-554.
    Vardanyan's theorem states that the set of PA-valid principles of Quantified Modal Logic, QML, is complete Π0 2. We generalize this result to a wide class of theories. The crucial step in the generalization is avoiding the use of Tennenbaum's Theorem.
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  17.  6
    Albert Visser (1992). An Inside View of Exp; or, the Closed Fragment of the Provability Logic of Iδ0 + Ω1 with a Propositional Constant for $\Operatorname{Exp}$. [REVIEW] Journal of Symbolic Logic 57 (1):131 - 165.
    In this paper I give a characterization of the closed fragment of the provability logic of I ▵0 + EXP with a propositional constant for EXP. In three appendices many details on arithmetization are provided.
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  18.  3
    Albert Visser (2011). Hume's Principle, Beginnings. Review of Symbolic Logic 4 (1):114-129.
    In this note we derive Robinsons Principle in the context of very weak theories of classes and relations.
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  19.  40
    Albert Visser (2009). Cardinal Arithmetic in the Style of Baron Von Münchhausen. Review of Symbolic Logic 2 (3):570-589.
    In this paper we show how to interpret Robinson’s arithmetic Q and the theory R of Tarski, Mostowski, and Robinson as theories of cardinals in very weak theories of relations over a domain.
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  20. J. van Eijck & Albert Visser (1994). Logic and Information Flow. Monograph Collection (Matt - Pseudo).
     
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  21.  31
    Albert Visser (1998). Contexts in Dynamic Predicate Logic. Journal of Logic, Language and Information 7 (1):21-52.
    In this paper we introduce a notion of context for Groenendijk & Stokhof's Dynamic Predicate Logic DPL. We use these contexts to give a characterization of the relations on assignments that can be generated by composition from tests and random resettings in the case that we are working over an infinite domain. These relations are precisely the ones expressible in DPL if we allow ourselves arbitrary tests as a starting point. We discuss some possible extensions of DPL and the way (...)
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  22.  11
    Albert Visser & Kees Vermeulen (1996). Dynamic Bracketing and Discourse Representation. Notre Dame Journal of Formal Logic 37 (2):321-365.
    In this paper we describe a framework for the construction of entities that can serve as interpretations of arbitrary contiguous chunks of text. An important part of the paper is devoted to describing stacking cells, or the proposed meanings for bracket-structures.
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  23.  25
    Joost J. Joosten & Albert Visser (2000). The Interpretability Logic of All Reasonable Arithmetical Theories. Erkenntnis 53 (1-2):3-26.
    This paper is a presentation of astatus quæstionis, to wit of the problemof the interpretability logic of all reasonablearithmetical theories.We present both the arithmetical side and themodal side of the question.Dedicated to Dick de Jongh on the occasion of his 60th birthday.
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  24.  2
    Albert Visser (1995). A Course on Bimodal Provability Logic. Annals of Pure and Applied Logic 73 (1):109-142.
    In this paper we study 1. the frame-theory of certain bimodal provability logics involving the reflection principle and we study2. certain specific bimodal logics with a provability predicate for a subtheory of Peano arithmetic axiomatized by a non-standardly finite number of axioms.
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  25.  13
    Albert Visser (1999). Rules and Arithmetics. Notre Dame Journal of Formal Logic 40 (1):116-140.
    This paper is concerned with the logical structure of arithmetical theories. We survey results concerning logics and admissible rules of constructive arithmetical theories. We prove a new theorem: the admissible propositional rules of Heyting Arithmetic are the same as the admissible propositional rules of Intuitionistic Propositional Logic. We provide some further insights concerning predicate logical admissible rules for arithmetical theories.
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  26. Albert Visser (2002). Substitutions of Σ10-Sentences: Explorations Between Intuitionistic Propositional Logic and Intuitionistic Arithmetic. Annals of Pure and Applied Logic 114 (1-3):227-271.
    This paper is concerned with notions of consequence. On the one hand, we study admissible consequence, specifically for substitutions of Σ 1 0 -sentences over Heyting arithmetic . On the other hand, we study preservativity relations. The notion of preservativity of sentences over a given theory is a dual of the notion of conservativity of formulas over a given theory. We show that admissible consequence for Σ 1 0 -substitutions over HA coincides with NNIL -preservativity over intuitionistic propositional logic . (...)
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  27.  53
    Jan van Eijck & Albert Visser, Stanford Encyclopedia of Philosophy.
    Notice: This PDF version was distributed by request to members of the Friends of the SEP Society and by courtesy to SEP content contributors. It is solely for their fair use. Unauthorized distribution is prohibited. To learn how to join the Friends of the..
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  28. Albert Visser (2001). Submodels of Kripke Models. Archive for Mathematical Logic 40 (4):277-295.
    A Kripke model ? is a submodel of another Kripke model ℳ if ? is obtained by restricting the set of nodes of ℳ. In this paper we show that the class of formulas of Intuitionistic Predicate Logic that is preserved under taking submodels of Kripke models is precisely the class of semipositive formulas. This result is an analogue of the Łoś-Tarski theorem for the Classical Predicate Calculus.In Appendix A we prove that for theories with decidable identity we can take (...)
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  29.  15
    Albert Visser (1984). The Provability Logics of Recursively Enumerable Theories Extending Peano Arithmetic at Arbitrary Theories Extending Peano Arithmetic. Journal of Philosophical Logic 13 (1):97 - 113.
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  30.  8
    Albert Visser (2015). The Arithmetics of a Theory. Notre Dame Journal of Formal Logic 56 (1):81-119.
    In this paper we study the interpretations of a weak arithmetic, like Buss’s theory $\mathsf{S}^{1}_{2}$, in a given theory $U$. We call these interpretations the arithmetics of $U$. We develop the basics of the structure of the arithmetics of $U$. We study the provability logic of $U$ from the standpoint of the framework of the arithmetics of $U$. Finally, we provide a deeper study of the arithmetics of a finitely axiomatized sequential theory.
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  31.  12
    Dick De Jongh, Rineke Verbrugge & Albert Visser (2011). Intermediate Logics and the de Jongh Property. Archive for Mathematical Logic 50 (1):197-213.
    We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.
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  32.  4
    Volker Halbach & Albert Visser (2014). Self-Reference in Arithmetic II. Review of Symbolic Logic 7 (4):692-712.
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  33.  33
    Albert Visser (2012). A Tractarian Universe. Journal of Philosophical Logic 41 (3):519-545.
    In this paper we develop a reconstruction of the Tractatus ontology. The basic idea is that objects are unsaturated and that Sachlagen are like molecules. Bisimulation is used for the proper individuation of the Sachlagen. We show that the ordering of the Sachlagen is a complete distributive, lattice. It is atomistic , i.e., each Sachlage is the supremum of the Sachverhalte below it. We exhibit three normal forms for Sachlagen: the bisimulation collapse, the canonical unraveling and the canonical bisimulation collapse. (...)
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  34.  29
    Rineke Verbrugge & Albert Visser (1994). A Small Reflection Principle for Bounded Arithmetic. Journal of Symbolic Logic 59 (3):785-812.
    We investigate the theory IΔ 0 + Ω 1 and strengthen [Bu86. Theorem 8.6] to the following: if NP ≠ co-NP. then Σ-completeness for witness comparison formulas is not provable in bounded arithmetic. i.e. $I\delta_0 + \Omega_1 + \nvdash \forall b \forall c (\exists a(\operatorname{Prf}(a.c) \wedge \forall = \leq a \neg \operatorname{Prf} (z.b))\\ \rightarrow \operatorname{Prov} (\ulcorner \exists a(\operatorname{Prf}(a. \bar{c}) \wedge \forall z \leq a \neg \operatorname{Prf}(z.\bar{b})) \urcorner)).$ Next we study a "small reflection principle" in bounded arithmetic. We prove that for (...)
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  35.  3
    Giovanna D'Agostino & Albert Visser (2002). Finality Regained: A Coalgebraic Study of Scott-Sets and Multisets. [REVIEW] Archive for Mathematical Logic 41 (3):267-298.
    In this paper we study iterated circular multisets in a coalgebraic framework. We will produce two essentially different universes of such sets. The unisets of the first universe will be shown to be precisely the sets of the Scott universe. The unisets of the second universe will be precisely the sets of the AFA-universe. We will have a closer look into the connection of the iterated circular multisets and arbitrary trees. RID=""ID="" Mathematics Subject Classification (2000): 03B45, 03E65, 03E70, 18A15, 18A22, (...)
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  36.  15
    Dick Jongh & Albert Visser (1991). Explicit Fixed Points in Interpretability Logic. Studia Logica 50 (1):39 - 49.
    The problem of Uniqueness and Explicit Definability of Fixed Points for Interpretability Logic is considered. It turns out that Uniqueness is an immediate corollary of a theorem of Smoryski.
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  37.  4
    Albert Visser (1992). An Inside View of Exp; or, The Closed Fragment of the Provability Logic of IΔ0+ Ω1 with a Propositional Constant For. Journal of Symbolic Logic 57 (1):131-165.
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  38.  11
    Albert Visser (1989). Peano's Smart Children: A Provability Logical Study of Systems with Built-in Consistency. Notre Dame Journal of Formal Logic 30 (2):161-196.
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  39.  31
    Alasdair Urquhart & Albert Visser (2010). Decorated Linear Order Types and the Theory of Concatenation. In F. Delon (ed.), Logic Colloquium 2007. Cambridge University Press 1.
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  40.  7
    Albert Visser (2014). Interpretability Degrees of Finitely Axiomatized Sequential Theories. Archive for Mathematical Logic 53 (1-2):23-42.
    In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory—like Elementary Arithmetic EA, IΣ1, or the Gödel–Bernays theory of sets and classes GB—have suprema. This partially answers a question posed by Švejdar in his paper (Commentationes Mathematicae Universitatis Carolinae 19:789–813, 1978). The partial solution of Švejdar’s problem follows from a stronger fact: the convexity of the degree structure of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory in the degree (...)
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  41.  1
    Albert Visser (1982). On the Completenes Principle: A Study of Provability in Heyting's Arithmetic and Extensions. Annals of Mathematical Logic 22 (3):263-295.
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  42.  18
    Albert Visser (2008). Closed Fragments of Provability Logics of Constructive Theories. Journal of Symbolic Logic 73 (3):1081-1096.
    In this paper we give a new proof of the characterization of the closed fragment of the provability logic of Heyting's Arithmetic. We also provide a characterization of the closed fragment of the provability logic of Heyting's Arithmetic plus Markov's Principle and Heyting's Arithmetic plus Primitive Recursive Markov's Principle.
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  43.  22
    Albert Visser (2002). The Donkey and the Monoid. Dynamic Semantics with Control Elements. Journal of Logic, Language and Information 11 (1):107-131.
    Dynamic Predicate Logic (DPL) is a variant of Predicate Logic introduced by Groenendijk and Stokhof. One rationale behind the introduction of DPL is that it is closer to Natural Language than ordinary Predicate Logic in the way it treats scope. In this paper I develop some variants of DPL that can more easily approximate Natural Language in some further aspects. Specifically I add flexibility in the treatment of polarity and and some further flexibility in the treatment of scope.
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  44.  2
    Dick de Jongh & Albert Visser (1993). Preface. Annals of Pure and Applied Logic 61 (1-2):1.
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  45.  13
    Albert Visser (1997). Dynamic Relation Logic is the Logic of DPL-Relations. Journal of Logic, Language and Information 6 (4):441-452.
    In this paper we prove that the principles in the languagewith relation composition and dynamic implication, valid forall binary relations, are the same ones as the principlesvalid when we restrict ourselves to DPL-relations,i.e. relations generated from conditions (tests) and resettings.
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  46.  4
    Sergei Artemov, George Boolos, Erwin Engeler, Solomon Feferman, Gerhard Jäger & Albert Visser (1995). Preface. Annals of Pure and Applied Logic 75 (1-2):1.
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  47.  13
    Marco Hollenberg & Albert Visser (1999). Dynamic Negation, the One and Only. Journal of Logic, Language and Information 8 (2):137-141.
    We consider the variety of Dynamic Relation Algebras V(DRA). We show that the monoid of an algebra in this variety determines dynamic negation uniquely.
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  48.  2
    V. Yu Shavrukov & Albert Visser (2014). Uniform Density in Lindenbaum Algebras. Notre Dame Journal of Formal Logic 55 (4):569-582.
    In this paper we prove that the preordering $\lesssim $ of provable implication over any recursively enumerable theory $T$ containing a modicum of arithmetic is uniformly dense. This means that we can find a recursive extensional density function $F$ for $\lesssim $. A recursive function $F$ is a density function if it computes, for $A$ and $B$ with $A\lnsim B$, an element $C$ such that $A\lnsim C\lnsim B$. The function is extensional if it preserves $T$-provable equivalence. Secondly, we prove a (...)
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  49.  8
    Albert Visser (1991). On the $\Sigma^01$-Conservativity of $\Sigma^01$-Completeness. Notre Dame Journal of Formal Logic 32 (4):554-561.
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  50.  8
    Albert Visser (2006). Propositional Logics of Closed and Open Substitutions Over Heyting's Arithmetic. Notre Dame Journal of Formal Logic 47 (3):299-309.
    In this note we compare propositional logics for closed substitutions and propositional logics for open substitutions in constructive arithmetical theories. We provide a strong example where these logics diverge in an essential way. We prove that for Markov's Arithmetic, that is, Heyting's Arithmetic plus Markov's principle plus Extended Church's Thesis, the logic of closed and the logic of open substitutions are the same.
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