The hypothesis of the conditional construal of conditional probability
Probability and conditionals
Every Linear Pseudo BL-Algebra Admits a State
Soft Computing - A Fusion of Foundations, Methodologies and Applications
A Presentation of Quantum Logic Based on an and then Connective
Journal of Logic and Computation
Pseudocomplemented lattice effect algebras and existence of states
Information Sciences: an International Journal
What is mathematical fuzzy logic
Fuzzy Sets and Systems
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An effect algebra is a partial algebraic structure, originally formulated as an algebraic base for unsharp quantum measurements. In this article we present an approach to the study of lattice effect algebras (LEAs) that emphasizes their structure as algebraic models for the semantics of (possibly) non-standard symbolic logics. This is accomplished by focusing on the interplay among conjunction, implication, and negation connectives on LEAs, where the conjunction and implication connectives are related by a residuation law. Special cases of LEAs are MV-algebras and orthomodular lattices. The main result of the paper is a characterization of LEAs in terms of so-called Sasaki algebras. Also, we compare and contrast LEAs, Hájek's BL-algebras, and the basic algebras of Chajda, Halaš, and Kühr.