Karim Nour, Christophe Raffalli
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
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Ken Pledger devised a one-sorted approach to the incidence relation of plane geometries, using structures that also support models of propositional modal logic. He introduced a modal system 12g that is valid in one-sorted projective planes, proved that it has finitely many non-equivalent modalities, and identified all possible modality patterns of its extensions. One of these extensions 8f is valid in elliptic planes. These results were presented in his doctoral dissertation [14], which has been reprinted in the Australasian Journal of Logic, vol. 18, no. 4. https://doi.org/10.26686/ajl.v18i4.…
The doctrinal Gödel's completeness theorem and the type space functor
研究在一阶布尔教义形式体系内自证哥德尔完备性定理，表明该定理使一阶布尔教义的纤维式斯通对偶成为类型空间函子，阐述了公式布尔代数对偶与模型斯通空间的关系。
In [Mon11] are studied, for the axiomatic extensions of the monoidal t-norm based logic ([EG01]), the properties of single chain completeness. On the other side, in [GJKO07, Chapter 5] are studied many logical and algebraic properties (like Halldén completeness, variable separation properties, amalgamation property etc.), in the context of substructural logics. The aim of this paper is twofold: first of all we will specialize the properties studied in [GJKO07, Chapter 5] from the case of substructural logics to the one of extensions of MTL, by obtaining some general characterization. Moreover …
Graph-Based Logic and Sketches II: Finite-Product Categories and Equational Logic (Preliminary Report)
本文表明，本文第一部分（见http：//www.cwru.edu/1/class/mans/math/pub/wells）中提供的草图和形式的证明论，足以产生Goguen和Meseguer的文章"多分类方程逻辑的完备性“（Technical Report CSL-135，SRI International Computer Science Laboratory，333 Ravenswood Ave.，门洛帕克，加利福尼亚州94025，美国，1982年）。
In the present paper syntax and semantics will be presented for an expansion of ordinary n-agent QML with constant domain, non-rigid constants, rigid variables and including both functions, relations, and equality. Further, the number of agents will be specified axiomatically thus ensuring maximal flexibility wrt. the cardinality of the set of agents. Domain, variables, and constants will be partitioned in an agent-part and an object-part and the syntax will be expanded to include strings in which indexes of modal operators are quantified over as wff's of the language. This will enhance expres…
Model theory of quasitracial $\mathrm{AW}^*$-algebras and the absoluteness of monotone completeness
该研究建立了拟迹AW*-代数的模型理论，将单调完备性猜想有限情形归约为II₁型AW*-因子的单调序列完备性，证明相关问题等价于算术Π⁰₂语句，并解答了实AW*-代数的若干开放问题。
Arithmetical completeness theorems for monotonic modal logics
本文研究了满足条件M的可证性谓词的模态逻辑性质，证明了五种单调模态逻辑的算术完全性定理，并从模态逻辑角度区分了一致性陈述的两种不同形式化。
Game logic was introduced by Rohit Parikh in the 1980s as a generalisation of propositional dynamic logic (PDL) for reasoning about outcomes that players can force in determined 2-player games. Semantically, the generalisation from programs to games is mirrored by moving from Kripke models to monotone neighbourhood models. Parikh proposed a natural PDL-style Hilbert system which was easily proved to be sound, but its completeness has thus far remained an open problem. In this paper, we introduce a cut-free sequent calculus for game logic, and two cut-free sequent calculi that manipulate annota…
This is the second in a series of articles surveying the body of work on the model theory of S-acts over a monoid S. The first concentrated on the theory of regular S-acts. Here we review the material on model-theoretic properties of free, projective, and (strongly, weakly) flat S-acts. We consider questions of axiomatizability, completeness, model completeness, and stability for these classes. Most but not all of the results have already appeared; we remark that the description of those monoids S such that the class of free left S-acts is axiomatizable, is new.
On the Multicategorical Meta-Theorem and the Completeness of Restricted Algebraic Deduction Systems
该研究在代数理论框架下建立8个范畴可靠性与完备性定理，构造上下文结构与结构范畴的双射对应及相关等式演绎系统，证明其在对应多范畴模型下的语义性质可转移。
A note on schematic validity and completeness in Prawitz's semantics
本文探讨两种单调性证明论语义路径，证明经典逻辑在基语义下的正确性可适配于允许非模式化辩护的SVA框架，同时指出模式化辩护要求可能导致该正确性失效，揭示辩护理解方式是证明论有效性解释的核心区分点。
A comparison of three kinds of monotonic proof-theoretic semantics and the base-incompleteness of intuitionistic logic
本文比较可归约性语义与基语义（含Sandqvist变体）三种单调证明论语义，建立二者间的转换条件，并据此讨论直觉主义逻辑的基完备性问题。
We analyse the pseudofinite monadic second order theory of words over a fixed finite alphabet. In particular we present an axiomatisation of this theory, working in a one-sorted first order framework. The analysis hinges on the fact that concatenation of words interacts nicely with monadic second order logic. More precisely, give a signature under which for each natural number k, equivalence of (monadic second order versions of) words with respect to formulas of quantifier depth at most k is a congruence for concatenation. We use our analysis to present an alternative proof of a theorem connec…
We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result considers the extension of dependence logic where Q is interpreted as "there exists uncountable many." Both of the axiomatizations are shown to be sound and complete for FO(Q) consequences.
Mechanising Gödel-Löb provability logic in HOL Light
该论文在HOL Light中形式化了Gödel-Löb可证性逻辑的元理论，证明可靠性与完备性，并实现了一个基于G3KGL演算的判定算法作为定理证明器策略。
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