In this paper, we propose a decidable single-agent modal logic for reasoning about goal-directed “knowing how”, based on ideas from linguistics, philosophy, modal logic, and automated planning in AI. We first define a modal language to express “I know how to guarantee \ given \” with a semantics based not on standard epistemic models but on labeled transition systems that represent the agent’s knowledge of his own abilities. The semantics is inspired by conformant planning in AI. A sound and complete (...) proof system is given to capture valid reasoning patterns, which highlights the compositional nature of “knowing how”. The logical language is further extended to handle knowing how to achieve a goal while maintaining other conditions. (shrink)

In this work we define contingency logic with arbitrary announcement. In contingency logic, the primitive modality contingency formalises that a proposition may be true but also may be false, so that if it is non-contingent then it is necessarily true or necessarily false. To this logic one can add dynamic operators to describe change of contingency. Our logic has operators for public announcement and operators for arbitrary public announcement, as in the dynamic epistemic logic called arbitrary public announcement logic. However, (...) our language primitive is the more suitable notion of public announcement whether, instead of the public announcement that. We compare the expressive power of our logic and its various fragments to related dynamic epistemic logics. We further present an axiomatisation and show its completeness by adapting a method to demonstrate completeness of arbitrary public announcement logic. Various extensions are also shown to be complete with respect to the corresponding frame classes. (shrink)

The paper aims at developing the idea that the standard operator of noncontingency, usually symbolized by Δ, is a special case of a more general operator of dyadic noncontingency Δ(−, −). Such a notion may be modally defined in different ways. The one examined in the paper is __Δ__(B, A) = df ◊B ∧ (A ⥽ B ∨ A ⥽ ¬B), where ⥽ stands for strict implication. The operator of dyadic contingency __∇__(B, A) is defined as the negation of __Δ__(B, (...) A). Possibility (◊A) may be then defined as __Δ__(A, A), necessity (□A) as __∇__(¬A, ¬A) and standard monadic noncontingency (__Δ__A) as __Δ__( \({\textsf{T}}\), A). In the second section it is proved that the deontic system KD is translationally equivalent to an axiomatic system of dyadic noncontingency named KDΔ 2, and that the minimal system KΔ of monadic contingency is a fragment of KDΔ 2. The last section suggests lines for further inquiries. (shrink)

The completeness of the axiomatization of contingency logic over symmetric frames has been thought of as a nontrivial job, the unimodal case of which cannot be generalized to the finitely multimodal case, which in turn cannot be generalized to the infinitely multimodal case. This paper deals with the completeness of symmetric contingency logic with unlimitedly many modalities, no matter whether the set of modalities is finite or infinite.

As shown in Fan, there are some similarities/resemblances between contingency and accident. Given this, one may naturally ask if we can unify the two operators to manifest all of their similarities/resemblances. In this article, instead of looking at the interactions between the two operators like in Fan, we turn our attention to the resemblances between the two operators. We extend the unification method in Fan to the current setting. The main results include some model-theoretical ones, such as expressivity, frame definability, (...) bisimulation, and some axiomatization ones. (shrink)

Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed up sometimes, in both daily life and academic research. This indicates that it is necessary to study them in a unified framework. However, there has been no logical research on them together. In this paper, we propose a language of a bimodal logic with these two concepts, investigate its model-theoretical properties such as expressivity and frame definability. We axiomatize this (...) logic over various classes of frames, whose completeness proofs are shown with the help of a crucial schema. The interactions between contingency and accident can sharpen our understanding of both notions. Then we extend the logic to a dynamic case: public announcements. By finding the required reduction axioms, we obtain a complete axiomatization, which gives us a good application to Moore sentences. (shrink)

In this paper, we introduce a notion of ‘disjunctive ignorance’, which is a weak combination of two forms of ignorance in the literature. We propose a logical language with ‘disjunctive ignorance’ as a sole modality, explore the logical properties of this notion and its related notions, and axiomatize it over various frame classes. By finding suitable reduction axioms, we extend the results to the case of public announcements and apply it to Moore-like sentences.