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A favorable business environment plays a crucial role in facilitating the high-quality development of a modern economy. In order to enhance the credibility and efficiency of business environment evaluation, this paper proposes a hybrid storage blockchain-based query efficiency enhancement method for business environment evaluation. Currently, most blockchain systems store block data in key-value databases or file systems with simple semantic descriptions. However, such systems have a single query interface, limited supported query types, and high storage overhead, which leads to low performance. To tackle these challenges, this paper proposes a query efficiency enhancement method based on hybrid storage blockchain. Firstly, data are stored in a hybrid data storage architecture combining on-chain and off-chain. Additionally, relational semantics are added to block data, and three index mechanisms are designed to expedite data access. Subsequently, corresponding query efficiency enhancement algorithms are designed based on the query types that are applicable to the aforementioned three index mechanisms, further refining the query processing. Finally, a comprehensive authentication query is implemented on the blockchain for the light client, and the user can verify the soundness and integrity of the query results. Experimental results on three open datasets show that the method proposed in this paper significantly reduces storage overhead, has shorter query latency for three different query types, and improves retrieval performance and verification efficiency. [ABSTRACT FROM AUTHOR]

Here I show that the one-variable fragment of several first-order relevant logics corresponds to certain S5ish extensions of the underlying propositional relevant logic. In particular, given a fairly standard translation between modal and one-variable languages and a permuting propositional relevant logic L, a formula A of the one-variable fragment is a theorem of LQ (QL) iff its translation is a theorem of L5 (L.5). The proof is model-theoretic. In one direction, semantics based on the Mares-Goldblatt [15] semantics for quantified L are transformed into ternary (plus two binary) relational semantics for S5-like extensions of L (for a general presentation, see Seki [26-27]). In the other direction, a valuation is given for the full first-order relevant logic based on L into a model for a suitable S5 extension of L. I also discuss this work's relation to finding a complete axiomatization of the constant domain, non-general frame ternary relational semantics for which RQ is incomplete [11]. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of connexive and bi-intuitionistic multilattices and develop on their base the algebraic semantics for Kamide, Shramko, and Wansing's connexive and bi-intuitionistic multilattice logics which were previously known in the form of sequent calculi and Kripke semantics. We prove that these logics are sound and complete with respect to the presented algebraic structures. [ABSTRACT FROM AUTHOR]

The present paper attempts to provide an exact truthmaker semantical analysis of modalized propositions. According to the present proposal, an exact truthmaker for "Necessarily P" is a state that bans every exact truthmaker for "Not P", and an exact truthmaker for "Possibly P" is a state that allows an exact truthmaker for P. Based on this proposal, a formal semantics will be developed; and the soundness and completeness results for a well-known family of the systems of normal modal propositional logic will be established. It shall be seen that the present analysis offers an exactification of the standard Kripke semantics in the sense that it analyzes the accessibility relation between possible worlds in terms of the banning and allowing relations between the constituent states, and thereby gives an account of "truth at a possible world" in terms of exact truthmaking. [ABSTRACT FROM AUTHOR]

The article "Quantification, matching and events" by Richard K. Larson discusses the topic of quantification and matching in natural language semantics. The author explores examples of quantification and argues that the truth conditions of these statements involve matching between different elements. The article proposes that matching in quantification arises from the internal semantic structure of the quantifier and suggests that all quantifiers can be analyzed as having an underlying structure involving injections into events. The author also addresses the role of context, the difference between unbound pronouns and variables bound by existential quantifiers, and different analyses of sentences involving quantification and matching. The text concludes by discussing the connection between quantification, matching, and events, and argues that events, injections, and matching are central to all quantification. The article also explores the need for quantificational states in the semantics of adverbial quantifiers and proposes a neo-Davidsonian approach to understanding quantification. The text discusses semantic rules for quantifiers and provides a framework for understanding quantification in natural language. Finally, the author discusses the topic of quantification in relation to adverbial quantification and argues that all quantifiers involve matching. [Extracted from the article]

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. p ⇒ q is thus defined as ¬ ◊ (p ∧ ¬ q) ∧ ◊ p ∧ ◊ ¬ q . We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle's theses and weak Boethius' thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut. [ABSTRACT FROM AUTHOR]

Falsification-aware (hyper)sequent calculi and Kripke semantics for normal modal logics including S4 and S5 are introduced and investigated in this study. These calculi and semantics are constructed based on the idea of a falsification-aware framework for Nelson's constructive three-valued logic. The cut-elimination and completeness theorems for the proposed calculi and semantics are proved. [ABSTRACT FROM AUTHOR]

This article compares classical (or KF-like) and nonclassical (or PKF-like) axiomatisations of the fixed-point semantics developed by Kripke (J Philos 72(19): 690–716, 1975). Following the line of investigation of Halbach and Nicolai (J Philos Logic 47(2): 227–257, 2018), we do not compare KF and PKF qua theories of truth simpliciter, but rather qua axiomatisations of the Kripkean conception of truth. We strengthen the central results of Halbach and Nicolai (2018) and Nicolai (Stud Log 106(1): 101–130, 2018), showing that, on the one hand, there is a stronger sense in which some variants of KF and some variants of PKF can be taken to be, truth-theoretically, equivalent. On the other hand, we show that this truth-theoretical equivalence is not preserved by some other variants of KF and PKF, arguing that the PKF variants are more adequate axiomatisations of the fixed-point semantics than the corresponding KF variants. [ABSTRACT FROM AUTHOR]

The joint logic of problems and propositions QHC introduced by S. A. Melikhov, as well as intuitionistic modal logic QH4, is studied. An immersion of these logics into classical first-order predicate logic is considered. An analog of the Löwenheim–Skolem theorem on the existence of countable elementary submodels for QHC and QH4 is established. [ABSTRACT FROM AUTHOR]

This paper proposes new semantics for propositional dynamic logic (PDL), replacing the standard relational semantics. Under these new semantics, program execution is represented as fundamentally deterministic (i.e., functional), while nondeterminism emerges as an epistemic relationship between the agent and the system: intuitively, the nondeterministic outcomes of a given process are precisely those that cannot be ruled out in advance. We formalize these notions using topology and the framework of dynamic topological logic (DTL) (Kremer and Mints in Ann Pure Appl Logic 131:133–158, 2005). We show that DTL can be used to interpret the language of PDL in a manner that captures the intuition above, and moreover that continuous functions in this setting correspond exactly to deterministic processes. We also prove that certain axiomatizations of PDL remain sound and complete with respect to the corresponding classes of dynamic topological models. Finally, we extend the framework to incorporate knowledge using the machinery of subset space logic (Dabrowski et al. in Ann Pure Appl Logic 78:73–110, 1996), and show that the topological interpretation of public announcements as given in Bjorndahl (in: van Ditmarsch and Sandu (eds) Jaakko Hintikka on knowledge and game theoretical semantics, outstanding contributions to Logic, vol 12, Springer, 2018) coincides exactly with a natural interpretation of test programs. [ABSTRACT FROM AUTHOR]

SQL is the world's most popular declarative language, forming the basis of the multi-billion-dollar database industry. Although SQL has been standardized, the full standard is based on ambiguous natural language rather than formal specification. Commercial SQL implementations interpret the standard in different ways, so that, given the same input data, the same query can yield different results depending on the SQL system it is run on. Even for a particular system, mechanically checked formalization of all widely-used features of SQL remains an open problem. The lack of a well-understood formal semantics makes it very difficult to validate the soundness of database implementations. Although formal semantics for fragments of SQL were designed in the past, they usually did not support set and bag operations, lateral joins, nested subqueries, and, crucially, null values. Null values complicate SQL's semantics in profound ways analogous to null pointers or side-effects in other programming languages. Since certain SQL queries are equivalent in the absence of null values, but produce different results when applied to tables containing incomplete data, semantics which ignore null values are able to prove query equivalences that are unsound in realistic databases. A formal semantics of SQL supporting all the aforementioned features was only proposed recently. In this paper, we report about our mechanization of SQL semantics covering set/bag operations, lateral joins, nested subqueries, and nulls, written in the Coq proof assistant, and describe the validation of key metatheoretic properties. Additionally, we are able to use the same framework to formalize the semantics of a flat relational calculus (with null values), and show a certified translation of its normal forms into SQL. [ABSTRACT FROM AUTHOR]

We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and generalizes two semantics already appearing in the literature: Aguzzoli, Bianchi, and Marra's temporal flow semantics for Hájek's basic logic, and Lewis-Smith, Oliva, and Robinson's semantics for intuitionistic Łukasiewicz logic. As a consequence of our general theory, we recover the soundness and completeness results of these prior studies in a uniform fashion, and extend them to infinitely-many other substructural logics. [ABSTRACT FROM AUTHOR]

In this paper, we give an alternative semantics to the non-normal logic of knowing how proposed by Fervari et al. (Proc IJCAI 2017:1031–1038, 2017), based on a class of Kripke neighborhood models with both the epistemic relations and neighborhood structures. This alternative semantics is inspired by the same quantifier alternation pattern of ∃ ∀ in the semantics of the know-how modality and the (monotonic) neighborhood semantics for the standard modality. We show that this new semantics is equivalent to the original Kripke semantics in terms of the validities. A key result is a representation theorem showing that the more abstract Kripke neighborhood models can be represented by the concrete Kripke models with action transitions modulo the valid formulas. We prove the completeness of the logic for the neighborhood semantics. The neighborhood semantics can be adapted to other variants of logics of knowing how. It provides us a powerful technical tool to study these logics while preserving the basic semantic intuition. [ABSTRACT FROM AUTHOR]