In this paper we study the propositional fragment ##IMG## [http://ej.iop.org/images/1064-5616/211/5/709/MSB_211_5_709ieqn1.gif] {$\mathrm{HC}$} of the joint logic of problems and propositions introduced by Melikhov. We provide Kripke semantics for this logic and show that ##IMG## [http://ej.iop.org/images/1064-5616/211/5/709/MSB_211_5_709ieqn1.gif] {$\mathrm{HC}$} is complete with respect to those models and has the finite model property. We consider examples of the use of ##IMG## [http://ej.iop.org/images/1064-5616/211/5/709/MSB_211_5_709ieqn1.gif] {$\mathrm{HC}$} -models usage. In particular, we prove that ##IMG## [http://ej.iop.org/images/1064-5616/211/5/709/MSB_211_5_709ieqn1.gif] {$\mathrm{HC}$} is a conservative extension of the logic ##IMG## [http://ej.iop.org/images/1064-5616/211/5/709/MSB_211_5_709ieqn2.gif] {$\mathrm{H4}$} . We also show that the logic ##IMG##

中文翻译：

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问题和命题逻辑的Kripke语义

在本文中，我们研究了命题片段## IMG ## [http://ej.iop.org/images/1064-5616/211/5/709/MSB_211_5_709ieqn1.gif] {$ \ mathrm {HC} $}梅利霍夫提出的问题和命题的联合逻辑。我们为此逻辑提供了Kripke语义，并显示了## IMG ## [http://ej.iop.org/images/1064-5616/211/5/709/MSB_211_5_709ieqn1.gif] {$ \ mathrm {HC} $ }关于这些模型是完整的，并且具有有限的模型属性。我们考虑使用## IMG ## [http://ej.iop.org/images/1064-5616/211/5/709/MSB_211_5_709ieqn1.gif] {$ \ mathrm {HC} $} -models的示例用法。特别是，我们证明## IMG ## [http://ej.iop.org/images/1064-5616/211/5/709/MSB_211_5_709ieqn1.gif] {$ \ mathrm {HC} $}是保守的逻辑的扩展## IMG ## [http://ej.iop.org/images/1064-5616/211/5/709/MSB_211_5_709ieqn2.gif] {$ \ mathrm {H4} $}。