insight - Logic and Formal Methods

### The Dangers of Subjective "Truths" and the Importance of Objective Reality

There is an objective reality that exists independently of our beliefs, and we must align our perspectives with facts rather than constructing our own subjective "truths".

### 일상 담화의 논리 공리화

일상 담화를 더 잘 모델링하기 위해 제안된 세 값 논리 OL은 고전 논리와 비교할 때 독특한 특성을 보인다. 이 논문에서는 OL과 그 구조적 동반자 sOL에 대한 다중 결론 및 단일 결론 Hilbert 스타일 공리화를 제시하고, sOL의 대수적 의미론을 밝힌다.

### Axiomatization and Algebraic Semantics of the Logic of Ordinary Discourse

The Logic of Ordinary Discourse (OL) is a three-valued propositional logic that challenges classical logic by rejecting some theses and accepting non-classically valid principles. The authors present modular and analytic Hilbert-style multiple-conclusion and single-conclusion axiomatizations for OL and its structural companion sOL, and investigate their algebraic semantics.

### 파괴적 등가 해결이 슈퍼포지션 계산법의 완전성에 미치는 영향

파괴적 등가 해결은 슈퍼포지션 계산법의 완전성을 파괴할 수 있지만, 제한된 변형 계산법에서는 완전성을 유지할 수 있다.

### Completeness and Limitations of Destructive Equality Resolution in the Superposition Calculus

The naive addition of Destructive Equality Resolution (DER) to the standard abstract redundancy concept renders the Superposition Calculus refutationally incomplete, but several restricted variants of the calculus are refutationally complete even with DER.

### Inductive Reasoning with Equality Predicates, Contextual Rewriting, and Variant-Based Simplification

This paper presents an inductive inference system that combines automated and explicit-induction theorem proving techniques to prove validity of formulas in the initial algebra of an order-sorted equational theory. The system uses advanced equational reasoning techniques, including equationally defined equality predicates, narrowing, constructor variant unification, variant satisfiability, order-sorted congruence closure, contextual rewriting, and ordered rewriting, all working modulo axioms.

### Establishing the Relative Completeness of Satisfaction-based Quantum Hoare Logic with While-Loop

This paper presents the first relatively complete satisfaction-based quantum Hoare logic (QHL) with while-loop, addressing a long-standing challenge since the inception of QHL in 2006.

### Cut Elimination for Cyclic Proofs in Temporal Logic

This work presents a syntactic cut-elimination procedure for a cyclic sequent calculus GKe that captures the modal logic MLe extended with the 'eventually' temporal operator.

### λ-계산과 조합 논리의 의미론적 해석: 클론, 닫힌 범주, 그리고 그 관계

이 논문은 λ-계산과 조합 논리의 의미론적 해석을 다루며, 클론, 닫힌 범주, 그리고 이들 사이의 관계를 설명한다.

### Semantic Interpretation and Syntactic Model of Simply-Typed Lambda Calculus Using Multi-Ary Structures

The multi-ary perspective provides a uniform framework to derive the semantic interpretation and syntactic model of simply-typed lambda calculus, along with soundness and completeness results, by factoring the unary categorical semantics through a more fundamental multi-ary structure.