Review of Symbolic Logic最新文献

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Ontological Purity for Formal Proofs 形式证明的本体论纯洁性

3区数学 Q1 LOGIC

Review of Symbolic Logic

Pub Date : 2023-11-13 DOI: 10.1017/s1755020323000333

Robin Martinot

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Non-Factive Kolmogorov Conditionalization 非活动Kolmogorov条件化

3区数学 Q1 LOGIC

Review of Symbolic Logic

Pub Date : 2023-10-31 DOI: 10.1017/s1755020323000345

Michael Rescorla

引用次数: 0

An algebraic proof of completeness for monadic fuzzy predicate logic mMTL 一元模糊谓词逻辑完备性的代数证明

3区数学 Q1 LOGIC

Review of Symbolic Logic

Pub Date : 2023-10-18 DOI: 10.1017/s1755020323000291

Jun Tao Wang, Hongwei Wu

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Decidable fragments of the Quantified argument calculus 量化论证演算的可判定片段

3区数学 Q1 LOGIC

Review of Symbolic Logic

Pub Date : 2023-09-29 DOI: 10.1017/s175502032300031x

Edi Pavlović, Norbert Gratzl

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ALGEBRAIC SEMANTICS FOR RELATIVE TRUTH, AWARENESS, AND POSSIBILITY 相对真、觉知和可能性的代数语义

3区数学 Q1 LOGIC

Review of Symbolic Logic

Pub Date : 2023-09-28 DOI: 10.1017/s1755020323000308

Evan Piermont

Abstract This paper puts forth a class of algebraic structures, relativized Boolean algebras (RBAs), that provide semantics for propositional logic in which truth/validity is only defined relative to a local domain. In particular, the join of an event and its complement need not be the top element. Nonetheless, behavior is locally governed by the laws of propositional logic. By further endowing these structures with operators—akin to the theory of modal Algebras—RBAs serve as models of modal logics in which truth is relative. In particular, modal RBAs provide semantics for various well-known awareness logics and an alternative view of possibility semantics.

摘要本文提出了一类代数结构——相对布尔代数(RBAs)，它为命题逻辑提供了语义，其中真值/有效性仅相对于局部域定义。特别是，事件及其补充的连接不必是顶部元素。尽管如此，行为是由命题逻辑法则局部支配的。通过进一步赋予这些结构算子——类似于模态代数理论——rba充当了真理是相对的模态逻辑的模型。特别是，模态rba为各种已知的感知逻辑和可能性语义的另一种视图提供语义。

引用次数: 0

CANONICITY IN POWER AND MODAL LOGICS OF FINITE ACHRONAL WIDTH 有限时宽的幂与模态逻辑的正则性

3区数学 Q1 LOGIC

Review of Symbolic Logic

Pub Date : 2023-03-22 DOI: 10.1017/s1755020323000060

ROBERT GOLDBLATT, IAN HODKINSON

Abstract We develop a method for showing that various modal logics that are valid in their countably generated canonical Kripke frames must also be valid in their uncountably generated ones. This is applied to many systems, including the logics of finite width, and a broader class of multimodal logics of ‘finite achronal width’ that are introduced here.

摘要:我们发展了一种方法来证明各种模态逻辑在其可数生成的规范Kripke框架中有效，也必须在其不可数生成的规范Kripke框架中有效。这适用于许多系统，包括有限宽度的逻辑，以及这里介绍的更广泛的“有限非历时宽度”的多模态逻辑。

引用次数: 0

Dynamic Hyperintensional Belief Revision - erratum 动态高强度信念修订-勘误

IF 0.6 3区数学 Q1 LOGIC

Review of Symbolic Logic

Pub Date : 2021-11-12 DOI: 10.1017/s1755020321000381

Aybüke Özgün, Francesco Berto

引用次数: 0

INDEPENDENCE PROOFS IN NON-CLASSICAL SET THEORIES 非经典集合论中的独立性证明

IF 0.6 3区数学 Q1 LOGIC

Review of Symbolic Logic

Pub Date : 2021-03-22 DOI: 10.1017/S1755020321000095

Sourav Tarafder, G. Venturi

In this paper we extend to non-classical set theories the standard strategy of proving independence using Boolean-valued models. This extension is provided by means of a new technique that, combining algebras (by taking their product), is able to provide product-algebra-valued models of set theories. In this paper we also provide applications of this new technique by showing that: (1) we can import the classical independence results to non-classical set theory (as an example we prove the independence of $mathsf {CH}$ ); and (2) we can provide new independence results. We end by discussing the role of non-classical algebra-valued models for the debate between universists and multiversists and by arguing that non-classical models should be included as legitimate members of the multiverse.

本文将布尔值模型证明独立性的标准策略推广到非经典集合理论中。这种扩展是通过一种新技术提供的，该技术结合代数(通过取它们的乘积)，能够提供集合理论的积代数值模型。在本文中，我们还提供了这种新技术的应用，证明了:(1)我们可以将经典的独立性结果引入到非经典集合论中(作为一个例子，我们证明了$mathsf {CH}$的独立性);(2)我们可以提供新的独立性结果。最后，我们讨论了非经典代数值模型在大学论者和多元论者之间争论中的作用，并论证了非经典模型应该被包括为多元宇宙的合法成员。

引用次数: 6

Formal Qualitative Probability 形式定性概率

IF 0.6 3区数学 Q1 LOGIC

Review of Symbolic Logic

Pub Date : 2020-02-20 DOI: 10.1017/s1755020319000480

Daniel Kian Mc Kiernan

Choices rarely deal with certainties; and, where assertoric logic and modal logic are insufficient, those seeking to be reasonable turn to one or more things called “probability.” These things typically have a shared mathematical form, which is an arithmetic construct. The construct is often felt to be unsatisfactory for various reasons. A more general construct is that of a preordering, which may even be incomplete, allowing for cases in which there is no known probability relation between two propositions or between two events. Previous discussion of incomplete preorderings has been as if incidental, with researchers focusing upon preorderings for which quantifications are possible. This article presents formal axioms for the more general case. Challenges peculiar to some specific interpretations of the nature of probability are brought to light in the context of these propositions. A qualitative interpretation is offered for probability differences that are often taken to be quantified. A generalization of Bayesian updating is defended without dependence upon coherence. Qualitative hypothesis testing is offered as a possible alternative in cases for which quantitative hypothesis testing is shown to be unsuitable.

选择很少涉及确定性;而且，在断言逻辑和模态逻辑不足的地方，那些寻求合理的人转向一个或多个被称为“概率”的东西。这些东西通常有一个共同的数学形式，这是一个算术结构。由于各种原因，这种结构常常不能令人满意。一个更一般的结构是预先排序，它甚至可能是不完整的，允许两个命题或两个事件之间没有已知概率关系的情况。先前关于不完全预排序的讨论似乎是偶然的，研究人员关注的是可能量化的预排序。本文为更一般的情况提供了形式公理。在这些命题的背景下，对概率本质的某些特定解释所特有的挑战被揭示出来。对于通常被量化的概率差异，提供了一种定性解释。在不依赖于相干性的情况下，对贝叶斯更新的概括进行了辩护。定性假设检验是提供作为一个可能的替代情况下，定量假设检验被证明是不合适的。

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引用次数: 0

Obligation as Weakest Permission: a strongly Complete Axiomatization 义务作为最弱许可:一个强完全公理化

IF 0.6 3区数学 Q1 LOGIC

Review of Symbolic Logic

Pub Date : 2016-06-01 DOI: 10.1017/S1755020316000034

F. Putte

In (Anglberger et al., 2015, Section 4.1), a deontic logic is proposed which explicates the idea that a formula φ is obligatory if and only if it is (semantically speaking) the weakest permission. We give a sound and strongly complete, Hilbert style axiomatization for this logic. As a corollary, it is compact, contradicting earlier claims from Anglberger et al. (2015). In addition, we prove that our axiomatization is equivalent to Anglberger et al.’s infinitary proof system, and show that our results are robust w.r.t. certain changes in the underlying semantics. §1. Intro. In Roy et al. (2014, 2012) and Anglberger et al. (2015), a logic is developed for “obligation as weakest permission”.1 The semantics proposed in Anglberger et al. (2015) is meant to capture the deontic aspects of reasoning in strategic games, where we speak about properties of the best actions available to a given agent. Whereas usually in formal models of such games, actions and/or agents are modeled explicitly at the object level, the present logic only speaks about action tokens (which correspond to states in a Kripke-model) and action types (sets of action tokens). Let us explain this briefly—we refer to the cited works for a more elaborate discussion. Consider a situation in which an agent can choose from a number of distinct action tokens, where at least some of these are optimal. Whereas the agent is permitted to perform one of those optimal action tokens, his sole obligation (if there is one at all – mind this important caveat) is to perform one of the optimal action tokens. This means that the deontic operators O and P can be read as follows, where φ refers to an arbitrary action type: Oφ: “φ is the (only) action type that is obligatory”, or more elaborately: “an action token is optimal if and only if it is of type φ” Pφ: “if an action is of type φ, then it is optimal” Anglberger et al. moreover introduce an alethic modality , which they interpret as a universal modality. φ thus means that all available action tokens are of type φ. They then propose what they call a “minimal logic” 5HD for these three operators. However, as they argue, 5HD only captures one half of the notion of “obligation as weakest permission”. That is, if φ is obligatory, then the logic stipulates that φ is the weakest permitted action type. The converse does not hold: something can be the weakest permitted action type without being obligatory. Received: September 30, 2015. 1 In more recent work Dong and Roy (2015); Van De Putte (2015), the logic is compared to other constructions in deontic logic. c © Association for Symbolic Logic, 2016 370 doi:10.1017/S1755020316000034 OBLIGATION AS WEAKEST PERMISSION 371 In the fourth section of Anglberger et al. (2015), a brief discussion of this converse direction is given, and it is shown how this translates to the semantics of 5HD. Let us call the resulting logic 5HD∗; it will be defined in Section 2. It is argued in Anglberger et al. (2015) that 5HD∗ is no

在(Anglberger et al.， 2015, Section 4.1)中，提出了一个道义逻辑，它解释了公式φ是强制性的，当且仅当它(从语义上讲)是最弱的许可。对于这个逻辑，我们给出了一个健全的、强完备的、希尔伯特式的公理化。作为推论，它是紧凑的，与Anglberger等人(2015)的早期主张相矛盾。此外，我们证明了我们的公理化等价于Anglberger等人的无限证明系统，并证明了我们的结果在底层语义的某些变化下是鲁棒的。§1。介绍。在Roy等人(2014,2012)和Anglberger等人(2015)中，开发了“义务作为最弱许可”的逻辑Anglberger等人(2015)提出的语义旨在捕捉战略博弈中推理的道义方面，我们在其中谈论给定代理可用的最佳行为的属性。尽管在这类游戏的正式模型中，行动和/或代理通常是在对象层面上明确建模的，但目前的逻辑只涉及行动标记(对应于kripke模型中的状态)和行动类型(行动标记集)。让我们简要地解释一下——我们参考引用的作品进行更详细的讨论。考虑这样一种情况:代理可以从许多不同的操作令牌中进行选择，其中至少有一些是最优的。尽管代理被允许执行其中一个最优动作令牌，但他唯一的义务(如果有的话——记住这个重要的警告)是执行其中一个最优动作令牌。这意味着义务算子O和P可以这样解读，其中φ指的是任意的动作类型:Oφ:“φ是(唯一)强制性的动作类型”，或者更详细地说:“一个动作标记当且仅当它是φ类型时是最优的”Pφ:“如果一个动作是φ类型，那么它是最优的”Anglberger等人进一步引入了一个真性模态，他们将其解释为一个普遍模态。因此φ意味着所有可用的动作令牌都是φ类型的。然后，他们为这三家运营商提出了他们所谓的“最小逻辑”5HD。然而，正如他们所言，5HD只体现了“义务即最弱许可”概念的一半。也就是说，如果φ是强制性的，那么逻辑规定φ是允许的最弱动作类型。反过来不持有:可以允许的最低动作类型没有必修课。收稿日期:2015年9月30日。1在最近的研究中，Dong和Roy (2015);Van De Putte(2015)，将逻辑与道义逻辑中的其他结构进行了比较。c©Association for Symbolic Logic, 2016 370 doi:10.1017/S1755020316000034 OBLIGATION AS weak PERMISSION 371在Anglberger等人(2015)的第四部分中，给出了对这个反向方向的简要讨论，并展示了如何将其转化为5HD的语义。让我们调用生成的逻辑5 hd∗;它将在第2节中定义。Anglberger等人(2015)认为5HD∗不是紧致的，并且具有无限规则(R-Conv)的证明系统被证明是(弱)健全和完备的。本文的主要目的是给出5HD *的一个健全且强完备的希尔伯特式公理化(第3节)。作为一个推论，这个推论关系是紧凑的，与前一段中提到的主张相矛盾。此外，我们证明Anglberger等人提出的证明系统等价于5HD *(第4节)。最后，我们证明这些结果可以推广到其他类似的“义务作为最弱许可”的逻辑(第5节)。§2。定义。本节的目的是修复符号;它不含新材料。看到Anglberger et al。(2015)的原始定义和符号。我们使用一个模态命题语言，它是通过闭合命题字母S = {p1, p2，…}和⊥的集合，在布尔连接¬，∨，∧，、≡和一元算子O, P下得到的。将生成的公式集称为W。我们对待¬,∨、⊥O, P,原始;∧，、，≡都是用通常的方式定义的。在剩余部分中，设元变量φ，ψ，…值域在W和，，…的任意成员上。W的任意子集。定义2.1。一个严格的约束性框架F是一个四元组< W, R, n P, nO >，其中W是一个非空集合(F的定义域)，R = W × W, n P: W→P (P (W))和nO:W→℘(℘(W)具备下列条件(或)如果X∪Y∈n P (W),那么X∈n P (W)和Y∈n P (W) (WP)如果X∈(W)和Y∈n P (W),然后Y⊆X (OP)如果没有∈(W),那么X∈n P (W) (OC)如果X∈(W),那么X =∅(Conv)如果X∈n P (W)和Y∈n P (W), Y⊆X, X∈(W)如果一个框架遵循上述所有条件除了(可能)(Conv),它只是一个道义框架。(严格)道义模型是一个(严格)道义框架F和一个赋值v，该赋值v将每个命题原子映射到F的定义域的一个子集。设M = < W, R, nO, n P, v >是一个(严格)道义模型，且W∈W。 M, w |⊥M, w | p iff w∈v (p) M, w |¬φ敌我识别M, w |φM, w |φ∨ψ敌我识别M, w |φ或M, w |ψM, w |φ敌我识别M, w ' |φ为所有w '∈R (w) M, w | Oφ敌我识别为φ为M∈(w)米,w | pφ敌我识别为φ为M∈n p (w),在为φ为M = {u∈w | M u |φ}。定义2.3。5HD∗φ iff对于所有严格的义务模型M:如果M, w | ψ对于所有ψ∈，则M, w | φ。372弗雷德里克·范德普特§3。5HD *的公理化。定义3.1。5HD∗-定理的集合是下列公理模式的所有实例集合的闭包:经典命题逻辑(S5) S5对于(EQO) (φ≡ψ)、(EQP) (φ≡ψ)、(Pφ≡Pψ) (FCP) P(ψ∨φ)、(Pψ∧Pφ)(应该- perm) Oφ、Pφ(应该-可以)Oφ、φ(最弱- perm) Oφ、(Pψ、(ψ、φ)) (tautperm) P、O、O、O、O、O、(Pψ、φ)的所有重言式:

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