• J. Log. Comput. (IF 0.803) Pub Date : 2021-01-22
Juan P Aguilera; Robert S Lubarsky

Feedback is oracle computability when the oracle consists exactly of the con- and divergence information about computability relative to that same oracle. Here we study two possible feedback hyperjumps and characterize each of them as the complete |$\varSigma _1$| set relative to a level of Gödel’s constructible hierarchy |$L$|⁠.

更新日期：2021-01-22
• J. Log. Comput. (IF 0.803) Pub Date : 2020-11-19
Artemov S, Nerode A.

This volume stems from the International Symposium on Logical Foundations of Computer Science (LFCS’18), held in Deerfield Beach, Florida, January 8 – 11, 2018. Subsequent to that meeting some of the speakers were invited to contribute to this volume.

更新日期：2021-01-15
• J. Log. Comput. (IF 0.803) Pub Date : 2021-01-07
Steffen Lewitzka

We introduce the concept of |$\textit{access-based}$| intuitionistic knowledge which relies on the intuition that agent |$i$| knows |$\varphi$| if |$i$| has found |$\textit{access to a proof}$| of |$\varphi$|⁠. Basic principles are distribution and factivity of knowledge as well as |$\square\varphi\rightarrow K_i\varphi$| and |$K_i(\varphi\vee\psi) \rightarrow (K_i\varphi\vee K_i\psi)$|⁠, where |$\square\varphi$|

更新日期：2021-01-07
• J. Log. Comput. (IF 0.803) Pub Date : 2020-12-29
Yasir Mahmood; Arne Meier; Johannes Schmidt

Abductive reasoning is a non-monotonic formalism stemming from the work of Peirce. It describes the process of deriving the most plausible explanations of known facts. Considering the positive version, asking for sets of variables as explanations, we study, besides the problem of wether there exists a set of explanations, two explanation size limited variants of this reasoning problem (less than or

更新日期：2020-12-29
• J. Log. Comput. (IF 0.803) Pub Date : 2020-12-23
Yanhong A Liu; Scott D Stoller

Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a unified language, DA logic, for design and analysis logic, based on the unifying founded semantics and constraint semantics, that supports the power and ease of programming

更新日期：2020-12-23
• J. Log. Comput. (IF 0.803) Pub Date : 2020-12-19
Hirohiko Kushida

Artemov (2019, The provability of consistency) offered the notion of constructive truth and falsity of arithmetical sentences in the spirit of Brouwer–Heyting–Kolmogorov semantics and its formalization, the logic of proofs. In this paper, we provide a complete description of constructive truth and falsity for Friedman’s constant fragment of Peano arithmetic. For this purpose, we generalize the constructive

更新日期：2020-12-21
• J. Log. Comput. (IF 0.803) Pub Date : 2020-12-19

Justification awareness models (JAMs) were proposed by S. Artemov as a tool for modelling epistemic scenarios such as Russell’s prime minister example. It was demonstrated that the sharpness and the single-conclusion property of a model play an essential role in the epistemic usage of JAMs. The problem to axiomatize these properties using the propositional justification language was left opened. We

更新日期：2020-12-21
• J. Log. Comput. (IF 0.803) Pub Date : 2020-09-29
Kašterović S, Ghilezan S.

AbstractFull 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

更新日期：2020-12-03
• J. Log. Comput. (IF 0.803) Pub Date : 2020-09-29
Diener H, Lubarsky R.

AbstractWe 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.11

更新日期：2020-12-03
• J. Log. Comput. (IF 0.803) Pub Date : 2020-09-25
Artemov S.

AbstractWe 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

更新日期：2020-12-03
• J. Log. Comput. (IF 0.803) Pub Date : 2020-09-25
Baaz M, Leitsch A, Lolic A.

AbstractWe 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

更新日期：2020-12-03
• J. Log. Comput. (IF 0.803) Pub Date : 2020-09-25
Brünnler K, Flumini D, Studer T.

AbstractBlockchains 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 $\mathsf{BCL}$

更新日期：2020-12-03
• J. Log. Comput. (IF 0.803) Pub Date : 2020-09-23
Hannula M, Kontinen J, Virtema J.

AbstractTeam 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

更新日期：2020-12-03
• J. Log. Comput. (IF 0.803) Pub Date : 2020-09-22
Pakhomov F, Zapryagaev A.

AbstractPresburger 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

更新日期：2020-12-03
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 |$\alpha 更新日期：2020-07-13 • J. Log. Comput. (IF 0.803) Pub Date : 2020-05-28 Nicolas Troquard To introduce agent-based technologies in real-world systems, one needs to acknowledge that the agents often have limited access to resources. They have to seek after resource objectives and compete for those resources. We introduce a class of resource games where resources and preferences are specified with the language of a resource-sensitive logic. The agents are endowed with a bag of resources and 更新日期：2020-07-13 • J. Log. Comput. (IF 0.803) Pub Date : 2020-05-25 Theofanis Aravanis; Pavlos Peppas; Mary-Anne Williams Parikh’s relevance-sensitive axiom (P) for belief revision is open to two different interpretations, i.e. the weak and the strong version of (P), both of which are plausible depending on the context. Given that strong (P) has not received the attention it deserves, in this article, an extended examination of it is conducted. In particular, we point out interesting properties of the semantic characterization 更新日期：2020-07-13 • J. Log. Comput. (IF 0.803) Pub Date : 2020-06-04 Marcelo E Coniglio; Aldo Figallo-Orellano; Ana C Golzio The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (i.e. logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special 更新日期：2020-06-04 • J. Log. Comput. (IF 0.803) Pub Date : 2020-06-03 Merlin Carl We consider notions of space by Winter [21, 22]. We answer several open questions about these notions, among them whether low space complexity implies low time complexity (it does not) and whether one of the equalities P=PSPACE, P|$_{+}=$|PSPACE|$_{+}$| and P|$_{++}=$|PSPACE|$_{++}$| holds for ITTMs (all three are false). We also show various separation results between space complexity classes for 更新日期：2020-06-03 • J. Log. Comput. (IF 0.803) Pub Date : 2020-04-22 Uri Andrews; Noah Schweber; Andrea Sorbi A computably enumerable equivalence relation (ceer) |$X$| is called self-full if whenever |$f$| is a reduction of |$X$| to |$X$|⁠, then the range of |$f$| intersects all |$X$|-equivalence classes. It is known that the infinite self-full ceers properly contain the dark ceers, i.e. the infinite ceers which do not admit an infinite computably enumerable transversal. Unlike the collection of dark ceers 更新日期：2020-04-22 • J. Log. Comput. (IF 0.803) Pub Date : 2020-04-16 MING HSIUNG We associate an elementary cellular automaton with a set of self-referential sentences, whose revision process is exactly the evolution process of that automaton. A simple but useful result of this connection is that a set of self-referential sentences is paradoxical, iff (the evolution process for) the cellular automaton in question has no fixed points. We sort out several distinct kinds of paradoxes 更新日期：2020-04-16 • J. Log. Comput. (IF 0.803) Pub Date : 2020-04-15 Dazhu Li In this article, we start with a two-player game that models communication under adverse circumstances in everyday life and study it from the perspective of a modal logic of graphs, where links can be deleted locally according to definitions available to the adversarial player. We first introduce a new language, semantics and some typical validities. We then formulate a new type of first-order translation 更新日期：2020-04-15 • J. Log. Comput. (IF 0.803) Pub Date : 2020-04-15 Rob Egrot We define an order polarity to be a polarity |$(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}})$| is an order polarity. We define a hierarchy of increasingly strong coherence conditions for extension 更新日期：2020-04-15 • J. Log. Comput. (IF 0.803) Pub Date : 2019-01-02 Stefan Hetzl; Sebastian Zivota We present formula equations—first-order formulas with unknowns standing for predicates—as a general formalism for treating certain questions in logic and computer science, like the Auflösungsproblem and loop invariant generation. In the case of the language of affine terms over |$\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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