In this article, we study modal extensions of Product fuzzy logic with both algebraic semantics and relational semantics based on Kripke structures with crisp accessibility relations, when the underlying product fuzzy logic is expanded with truth-constants, the Δ operator and with two infinitary inference rules. We provide completeness results for both kinds of semantics. Finally, we also consider a generalization of possibilistic logic evaluated over product algebras. © The Author, 2015. Published by Oxford University Press. All rights reserved.

The authors wish to thank the anonymous reviewers for their valuable comments and suggestions that have significantly improved the article. They also thank Félix Bou and Tommaso Moraschini for helpful comments on Section 5. The authors acknowledge support of the Spanish projects EdeTRI (TIN2012-39348- C02-01) and 2014 SGR 118. Vidal was supported by a CSIC grant JAE Predoc.

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