arXiv subjects

Xuefeng Wen

Publications and source records attributed to Xuefeng Wen.

4 recordsLinked to original sources

arXiv2026

Stratified Counterpossible Logic

This paper presents two logic systems, SCP and its extension SCP1, to distinguish between different types of impossibility. The semantics use a stratified structure that partitions worlds into logic-normal worlds (N) and anti-logic worlds (I). By defining a metaphysical accessibility relation within N, the systems separate metaphysical impossibility from logical contradiction. This allows for logical reasoning to be maintained even when dealing with metaphysical impossibilities. To address the challenge of vacuism, SCP1 implements a non-empty constraint on the selection function, ensuring that counterpossibles with impossible antecedents are not trivially true but depend on the connection between the antecedent and the consequent. We provide proofs for the soundness, completeness, and decidability of both systems. Finally, we indicate the possibility of applying this stratified approach to other modal domains, such as deontic or epistemic logic.

cs.LO↗

arXiv2020

Some Common Mistakes in the Teaching and Textbooks of Modal Logic

We discuss four common mistakes in the teaching and textbooks of modal logic. The first one is missing the axiom $\Diamondφ\leftrightarrow\neg\Box\negφ$, when choosing $\Diamond$ as the primitive modal operator, misunderstanding that $\Box$ and $\Diamond$ are symmetric. The second one is forgetting to make the set of formulas for filtration closed under subformulas, when proving the finite model property through filtration, neglecting that $\Boxφ$ and $\Diamondφ$ may be abbreviations of formulas. The third one is giving wrong definitions of canonical relations in minimal canonical models that are unmatched with the primitive modal operators. The final one is misunderstanding the rule of necessitation, without knowing its distinction from the rule of modus ponens. To better understand the rule of necessitation, we summarize six ways of defining deductive consequence in modal logic: omitted definition, classical definition, ternary definition, reduced definition, bounded definition, and deflationary definition, and show that the last three definitions are equivalent to each other.

cs.LO↗

arXiv2019

On Axiomatization of Lewis' Conditional Logics

This paper first shows that the popular axiomatic systems proposed by Nute for Lewis' conditional logics are not equivalent to Lewis' original systems. In particular, the axiom CA which is derivable in Lewis' systems is not derivable in Nute's systems. Then the paper proposes a new set of axiomatizations for Lewis' conditional logics, without using CSO, or RCEA, or the rule of interchange of logical equivalents. Instead, the new axiomatizations adopt two axioms which correspond to cautious monotonicity and cautious cut in nonmonotonic logics, respectively. Finally, the paper gives a simple resolution to a puzzle about the controversial axiom of simplification of disjunctive antecedents, using a long neglected axiom in one of Lewis' systems for conditional logics.

cs.LO↗

arXiv2019

Modal Logic via Global Consequence

In modal logic, semantic consequence is usually defined locally by truth preservation at all worlds in all models (with respect to a class of frames). It can also be defined globally by truth preservation in all models (with respect to a class of frames). The latter is called global consequence, which is much less studied than the standard local one. In this paper we first study the relationship between local and global consequence. Then we give some correspondence results for global consequence. Finally, we illustrate two applications of global consequence, connecting it with informational consequence and update consequence proposed in formal semantics. Some results in the paper are already known, which are collected in the paper for the sake of completeness. The others appear to be new. We suggest that global consequence is not only interesting theoretically, but also useful for application.

cs.LO↗