Abstract
In [6, 9] the authors have shown how to combine propositional BDI logics using Gabbay’s fibring methodology and in [11, 10] they outlined a tableaux proof procedure for the fibred BDI logic. In this paper we provide a proof related to completeness preservation of the combined BDI logic in the presence of interaction axioms of the form □1 ϕ⇒□2 ϕ in terms of canonical models. To be more precise, let Λ a , Λ b , Λ c , Λ d be canonical normal modal logics and \(\Lambda_{abcd} = \Lambda_{a} \circledcirc \Lambda_{b} \circledcirc \Lambda_{c} \circledcirc \Lambda_{d}\) be the logics obtained by fibring/dovetailing Λ a , Λ b , Λ c , Λ d . Then we show that \(\Lambda_{abcd} \oplus \Diamond_{a} \Box_{b} \varphi \Rightarrow \Box_{c} \Diamond_{d} \varphi\) is characterised by the class of fibred models satisfying the condition ∀ ω ∈ W,∀ \(\mathfrak{f} \in\) F, \(\mathfrak{M}^{ac}\)(ω) \(\sqsubseteq_{N}\) \(\mathfrak{M}^{bd}(\omega)\).
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Padmanabhan, V., Governatori, G., Sattar, A. (2011). Fibred BDI Logics: Completeness Preservation in the Presence of Interaction Axioms. In: Sombattheera, C., Agarwal, A., Udgata, S.K., Lavangnananda, K. (eds) Multi-disciplinary Trends in Artificial Intelligence. MIWAI 2011. Lecture Notes in Computer Science(), vol 7080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25725-4_6
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DOI: https://doi.org/10.1007/978-3-642-25725-4_6
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