Hybrid Logic Meets IF Modal Logic
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- 作者：Tero Tulenheimo
- 关键词：Compositionality ; Decidability ; Expressive power ; Game ; theoretic semantics ; Hybrid logic ; Independence friendly logic ; Modal logic
- 刊名：Journal of Logic ; Language and Information
- 出版时间：October, 2009
- 出版年：2009
- 期刊代码：83_09258531
- 类别：bio
- 卷：18
- 期：4
- 页码：559-591
- 数据来源：sp
摘要
The hybrid logic H(@,炉){\mathcal{H}(@,\downarrow)} and the independence friendly modal logic IFML are compared for their expressive powers. We introduce a logic IFML c having a non-standard syntax and a compositional semantics; in terms of this logic a syntactic fragment of IFML is singled out, denoted IFML c . (In the Appendix it is shown that the game-theoretic semantics of IFML c coincides with the compositional semantics of IFML c .) The hybrid logic H(@,炉){\mathcal{H}(@,\downarrow)} is proven to be strictly more expressive than IFML c . By contrast, H(@,炉){\mathcal{H}(@,\downarrow)} and the full IFML are shown to be incomparable for their expressive powers. Building on earlier research (Tulenheimo and Sevenster 2006), a PSPACE-decidable fragment of the undecidable logic H(@,炉){\mathcal{H}(@,\downarrow)} is disclosed. This fragment is not translatable into the hybrid logic H(@){\mathcal{H}(@)} and has not been studied previously in connection with hybrid logics. In the Appendix IFML c is shown to lack the property of ‘quasi-positionality’ but proven to enjoy the weaker property of ‘bounded quasi-positionality’. The latter fact provides from the IFML internal perspective an account of what makes the compositional semantics of IFML c possible.