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  • On uniform belief revision
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-18
    Aravanis T.

    AbstractRational belief-change policies are encoded in the so-called AGM revision functions, defined in the prominent work of Alchourrón, Gärdenfors and Makinson. The present article studies an interesting class of well-behaved AGM revision functions, called herein uniform-revision operators (or UR operators, for short). Each UR operator is uniquely defined by means of a single total preorder over

    更新日期:2020-10-13
  • Fraïssé–Hintikka theorem in institutions
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-03
    Daniel Găină; Tomasz Kowalski

    We generalize the characterization of elementary equivalence by Ehrenfeucht–Fraïssé games to arbitrary institutions whose sentences are finitary. These include many-sorted first-order logic, higher-order logic with types, as well as a number of other logics arising in connection to specification languages. The gain for the classical case is that the characterization is proved directly for all signatures

    更新日期:2020-10-13
  • Algorithmic properties of first-order modal logics of finite Kripke frames in restricted languages
    J. Log. Comput. (IF 0.803) Pub Date : 2020-08-26
    Mikhail Rybakov; Dmitry Shkatov

    We study the effect of restricting the number of individual variables, as well as the number and arity of predicate letters, in languages of first-order predicate modal logics of finite Kripke frames on the logics’ algorithmic properties. A finite frame is a frame with a finite set of possible worlds. The languages we consider have no constants, function symbols or the equality symbol. We show that

    更新日期:2020-10-13
  • A model-theoretic approach to descriptive general frames: the van Benthem characterization theorem
    J. Log. Comput. (IF 0.803) Pub Date : 2020-08-26
    Nick Bezhanishvili; Tim Henke

    The celebrated van Benthem characterization theorem states that on Kripke structures modal logic is the bisimulation-invariant fragment of first-order logic. In this paper, we prove an analogue of the van Benthem characterization theorem for models based on descriptive general frames. This is an important class of general frames for which every modal logic is complete. These frames can be represented

    更新日期:2020-10-13
  • Sublattices and Δ-blocks of orthomodular posets
    J. Log. Comput. (IF 0.803) Pub Date : 2020-07-28
    Chajda I, Länger H.

    AbstractStates of quantum systems correspond to vectors in a Hilbert space and observations to closed subspaces. Hence, this logic corresponds to the algebra of closed subspaces of a Hilbert space. This can be considered as a complete lattice with orthocomplementation, but it is not distributive. It satisfies a weaker condition, the so-called orthomodularity. Later on, it was recognized that joins

    更新日期:2020-10-13
  • Locally constant constructive functions and connectedness of intervals
    J. Log. Comput. (IF 0.803) Pub Date : 2020-07-20
    Chernov V.

    AbstractWe prove that every locally constant constructive function on an interval is in fact a constant function. This answers a question formulated by Andrej Bauer [ 1]. As a related result, we show that an interval consisting of constructive real numbers is in fact connected but can be decomposed into the disjoint union of two sequentially closed nonempty sets.

    更新日期:2020-10-13
  • Kripke-style Semantics and Completeness for Full Simply Typed Lambda Calculus
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-29
    Simona Kašterović; Silvia Ghilezan

    Full simply typed lambda calculus is the simply typed lambda calculus extended with product types and sum types. We propose a Kripke-style semantics for full simply typed lambda calculus. We then prove soundness and completeness of type assignment in full simply typed lambda calculus with respect to the proposed semantics. The key point in the proof of completeness is the notion of a canonical model

    更新日期:2020-09-29
  • Modeling legal conflict resolution based on dynamic logic
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-29
    Fengkui Ju; Karl Nygren; Tianwen Xu

    Conflicts between legal norms are common in reality. In many legislations, legal conflicts between norms are resolved by applying ordered principles. This work presents a formalization of the conflict resolution mechanism and introduces action legal logic (⁠|$\textsf{ALL}$|⁠) to reason about the normative consequences of possibly conflicting legal systems. The semantics of |$\textsf{ALL}$| is explicitly

    更新日期:2020-09-29
  • Notions of Cauchyness and metastability
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-29
    Hannes Diener; Robert Lubarsky

    We show that several weakenings of the Cauchy condition are all equivalent under the assumption of countable choice, and investigate to what extent choice is necessary. We also show that the syntactically reminiscent notion of metastability allows similar variations, but is empty in terms of its constructive content.1

    更新日期:2020-09-29
  • No false grounds and topology of argumentation
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-26
    Chenwei Shi

    We integrate Dung’s argumentation framework with a topological space to formalize Clark’s no false lemmas theory for solving the Gettier problem and study its logic. Our formalization shows that one of the two notions of knowledge proposed by Clark, justified belief with true grounds, satisfies Stalnaker’s axiom system of belief and knowledge except for the axiom of closure under conjunction. We propose

    更新日期:2020-09-26
  • Justification awareness
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-25
    Sergei Artemov

    We offer a new semantic approach to formal epistemology that incorporates two principal ideas: (i) justifications are prime objects of the model: knowledge and belief are defined evidence-based concepts; (ii) awareness restrictions are applied to justifications rather than to propositions, which allows for the maintaining of desirable closure properties. The resulting structures, Justification Awareness

    更新日期:2020-09-26
  • An abstract form of the first epsilon theorem
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-25
    Matthias Baaz; Alexander Leitsch; Anela Lolic

    We present a new method of computing Herbrand disjunctions. The up-to-date most direct approach to calculate Herbrand disjunctions is based on Hilbert’s epsilon formalism (which is in fact also the oldest framework for proof theory). The algorithm to calculate Herbrand disjunctions is an integral part of the proof of the extended first epsilon theorem. This paper introduces a more abstract form of

    更新日期:2020-09-25
  • A logic of blockchain updates
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-25
    Kai Brünnler; Dandolo Flumini; Thomas Studer

    Blockchains are distributed data structures that are used to achieve consensus in systems for cryptocurrencies (like Bitcoin) or smart contracts (like Ethereum). Although blockchains gained a lot of popularity recently, there are only few logic-based models for blockchains available. We introduce |$\mathsf{BCL}$|⁠, a dynamic logic to reason about blockchain updates, and show that |$\mathsf{BCL}$| is

    更新日期:2020-09-25
  • Classical term-modal logics
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-24
    Stef Frijters; Frederik Van De Putte

    We introduce classical term-modal logics and argue that they are useful for modelling agent-relative notions of obligation, evidence and abilities, and their interaction with properties of and relations between the agents in question. We spell out the semantics of these logics in terms of neighborhood models, provide sound and strongly complete axiomatizations and establish the decidability of specific

    更新日期:2020-09-24
  • Operator algebras with hyperarithmetic theory
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-23
    Isaac Goldbring; Bradd Hart

    We show that the following operator algebras have hyperarithmetic theory: the hyperfinite II|$_1$| factor |$\mathcal R$|⁠, |$L(\varGamma )$| for |$\varGamma $| a finitely generated group with solvable word problem, |$C^*(\varGamma )$| for |$\varGamma $| a finitely presented group, |$C^*_\lambda (\varGamma )$| for |$\varGamma $| a finitely generated group with solvable word problem, |$C(2^\omega )$|

    更新日期:2020-09-24
  • Polyteam semantics
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-23
    Miika Hannula; Juha Kontinen; Jonni Virtema

    Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define Polyteam Semantics in which formulae are evaluated over a family of teams. We begin

    更新日期:2020-09-23
  • Multi-dimensional Interpretations of Presburger Arithmetic in Itself
    J. Log. Comput. (IF 0.803) Pub Date : 2020-09-22
    Fedor Pakhomov; Alexander Zapryagaev

    Presburger arithmetic is the true theory of natural numbers with addition. We study interpretations of Presburger arithmetic in itself. The main result of this paper is that all self-interpretations are definably isomorphic to the trivial one. Here we consider interpretations that might be multi-dimensional. We note that this resolves a conjecture by Visser (1998, An overview of interpretability logic

    更新日期:2020-09-22
  • Corrigendum to: Displaying updates in logic
    J. Log. Comput. (IF 0.803) Pub Date : 2020-08-04
    Guillaume Aucher

    The first set of corrections concerns dual update logic. There was a typographical mistake in the truth conditions of the dual connectives: "y" and "z" should be swapped. The inference rules of the corresponding proof system in Figure 11 had also to be corrected. The second related set of corrections concerns the case study of section 8. It now only deals with intuitionistic logic and not with bi-intuitionistic

    更新日期:2020-08-19
  • On Scott’s semantics for many-valued logic
    J. Log. Comput. (IF 0.803) Pub Date : 2020-07-21
    Satoru Niki; Peter Schuster

    The semantics in ordered abelian groups Scott proposed for Łukasiewicz’s many-valued logic fails to be sound for one direction of one of the rules Scott gave for implication. We show this by a counterexample Urquhart has used to justify that in his own semantics, every formula has to have a least point at which it is valid. While this condition would make Scott’s semantics sound, it would cause a problem

    更新日期:2020-08-19
  • Convergence, continuity, recurrence and Turing completeness in dynamic epistemic logic
    J. Log. Comput. (IF 0.803) Pub Date : 2020-07-21
    Dominik Klein; Rasmus K Rendsvig

    The paper analyses dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence

    更新日期:2020-08-19
  • Ordered models for concept representation
    J. Log. Comput. (IF 0.803) Pub Date : 2020-07-20
    Michael Freund

    Basic notions linked with concept theory can be accounted for by partial order relations. These orders translate the fact that, for an agent, an object may be seen as a better or a more typical exemplar of a concept than anyother. They adequately model notions linked with categorial membership, typicality and resemblance, without any of the drawbacks that are classically encountered in conjunction

    更新日期:2020-08-19
  • Rational coordination with no communication or conventions
    J. Log. Comput. (IF 0.803) Pub Date : 2020-07-11
    Valentin Goranko; Antti Kuusisto; Raine Rönnholm

    We study pure coordination games where in every outcome, all players have identical payoffs, ‘win’ or ‘lose’. We identify and discuss a range of ‘purely rational principles’ guiding the reasoning of rational players in such games and compare the classes of coordination games that can be solved by such players with no preplay communication or conventions. We observe that it is highly nontrivial to delineate

    更新日期:2020-08-19
  • The generalized orthomodularity property: configurations and pastings
    J. Log. Comput. (IF 0.803) Pub Date : 2020-06-23
    Ivan Chajda; Davide Fazio; Antonio Ledda

    In this paper, we consider a generalization of the notion of orthomodularity for posets to the concept of the generalized orthomodularity property (GO-property) by considering the |$LU$|-operators. This seemingly mild generalization of orthomodular posets and its order theoretical analysis yield rather strong application to effect algebras and orthomodular structures. Also, for several classes of orthoalgebras

    更新日期:2020-07-13
  • On the different types of collective attacks in abstract argumentation: equivalence results for SETAFs
    J. Log. Comput. (IF 0.803) Pub Date : 2020-06-22
    Wolfgang Dvořák; Anna Rapberger; Stefan Woltran

    Argumentation frameworks with collective attacks are a prominent extension of Dung’s abstract argumentation frameworks, where an attack can be drawn from a set of arguments to another argument. These frameworks are often abbreviated as SETAFs. Although SETAFs have received increasing interest recently, a thorough study on the actual behaviour of collective attacks has not been carried out yet. In particular

    更新日期:2020-07-13
  • Sette’s calculus P1 and some hierarchies of paraconsistent systems
    J. Log. Comput. (IF 0.803) Pub Date : 2020-06-02
    Janusz Ciuciura

    The necessary condition for a calculus to be paraconsistent is that its consequence relation is not explosive. This results in rejection of the principle of ex contradictione sequitur quodlibet. In 1973, Sette presented a calculus, denoted as |$P^1$|⁠, which is paraconsistent only at the atomic level, i.e. |$\alpha $| and |${\sim }\alpha $| yield any |$\beta $| if, and only if the formula |$\alpha

    更新日期:2020-07-13
  • Individual resource games and resource redistributions
    J. Log. Comput. (IF 0.803) Pub Date : 2020-05-28
    Nicolas Troquard

    To introduce agent-based technologies in real-world systems, one needs to acknowledge that the agents often have limited access to resources. They have to seek after resource objectives and compete for those resources. We introduce a class of resource games where resources and preferences are specified with the language of a resource-sensitive logic. The agents are endowed with a bag of resources and

    更新日期:2020-07-13
  • A study of possible-worlds semantics of relevance-sensitive belief revision
    J. Log. Comput. (IF 0.803) Pub Date : 2020-05-25
    Theofanis Aravanis; Pavlos Peppas; Mary-Anne Williams

    Parikh’s relevance-sensitive axiom (P) for belief revision is open to two different interpretations, i.e. the weak and the strong version of (P), both of which are plausible depending on the context. Given that strong (P) has not received the attention it deserves, in this article, an extended examination of it is conducted. In particular, we point out interesting properties of the semantic characterization

    更新日期:2020-07-13
  • First-order swap structures semantics for some logics of formal inconsistency
    J. Log. Comput. (IF 0.803) Pub Date : 2020-06-04
    Marcelo E Coniglio; Aldo Figallo-Orellano; Ana C Golzio

    The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (i.e. logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special

    更新日期:2020-06-04
  • Space and time complexity for infinite time Turing machines
    J. Log. Comput. (IF 0.803) Pub Date : 2020-06-03
    Merlin Carl

    We consider notions of space by Winter [21, 22]. We answer several open questions about these notions, among them whether low space complexity implies low time complexity (it does not) and whether one of the equalities P=PSPACE, P|$_{+}=$|PSPACE|$_{+}$| and P|$_{++}=$|PSPACE|$_{++}$| holds for ITTMs (all three are false). We also show various separation results between space complexity classes for

    更新日期:2020-06-03
  • Self-full ceers and the uniform join operator
    J. Log. Comput. (IF 0.803) Pub Date : 2020-04-22
    Uri Andrews; Noah Schweber; Andrea Sorbi

    A computably enumerable equivalence relation (ceer) |$X$| is called self-full if whenever |$f$| is a reduction of |$X$| to |$X$|⁠, then the range of |$f$| intersects all |$X$|-equivalence classes. It is known that the infinite self-full ceers properly contain the dark ceers, i.e. the infinite ceers which do not admit an infinite computably enumerable transversal. Unlike the collection of dark ceers

    更新日期:2020-04-22
  • Elementary cellular automata and self-referential paradoxes
    J. Log. Comput. (IF 0.803) Pub Date : 2020-04-16
    MING HSIUNG

    We associate an elementary cellular automaton with a set of self-referential sentences, whose revision process is exactly the evolution process of that automaton. A simple but useful result of this connection is that a set of self-referential sentences is paradoxical, iff (the evolution process for) the cellular automaton in question has no fixed points. We sort out several distinct kinds of paradoxes

    更新日期:2020-04-16
  • Losing connection: the modal logic of definable link deletion
    J. Log. Comput. (IF 0.803) Pub Date : 2020-04-15
    Dazhu Li

    In this article, we start with a two-player game that models communication under adverse circumstances in everyday life and study it from the perspective of a modal logic of graphs, where links can be deleted locally according to definitions available to the adversarial player. We first introduce a new language, semantics and some typical validities. We then formulate a new type of first-order translation

    更新日期:2020-04-15
  • Order polarities
    J. Log. Comput. (IF 0.803) Pub Date : 2020-04-15
    Rob Egrot

    We define an order polarity to be a polarity |$(X,Y,{\operatorname{R}})$| where |$X$| and |$Y$| are partially ordered, and we define an extension polarity to be a triple |$(e_X,e_Y,{\operatorname{R}})$| such that |$e_X:P\to X$| and |$e_Y:P\to Y$| are poset extensions and |$(X,Y,{\operatorname{R}})$| is an order polarity. We define a hierarchy of increasingly strong coherence conditions for extension

    更新日期:2020-04-15
  • Decidability of affine solution problems
    J. Log. Comput. (IF 0.803) Pub Date : 2019-01-02
    Stefan Hetzl; Sebastian Zivota

    We present formula equations—first-order formulas with unknowns standing for predicates—as a general formalism for treating certain questions in logic and computer science, like the Auflösungsproblem and loop invariant generation. In the case of the language of affine terms over |$\mathbb{Q}$|⁠, we translate a quantifier-free formula equation into an equivalent statement about affine spaces over |$\mathbb{Q}$|⁠

    更新日期:2019-01-02
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