Sylvan was instrumental in the development and study of relevance logic. In 1972, Sylvan proposed a semantics for certain relevant logics that had been developed by American philosophersNuel Belnap and Alan Ross Anderson. Together with Robert K. Meyer, Routley turned this into a semantics for a large number of logical systems. Their work in logic work helped make ANU a center for the study of non-classical logic in general. Routley's work had particular influence for Graham Priest, a well-known proponent of non-classical logic; Sylvan and Priest edited a well-regarded volume on the topic. Priest in turn influenced Sylvan; they met in 1976 at the Australasian Association of Logic conference in Canberra at a time when Sylvan was doing novel work on dialetheism, the view that some contradictions are true. Not long after meeting Priest, then investigating a logic capable of handling such true contradictions, Sylvan also endorsed the view. Sylvan's studies ranged over a variety of topics in logic and the philosophy of logic. He wrote important papers on free logic, general modal logic, and natural deduction systems. However, much of his most important work in logic was dedicated to relevant logic, for which he authored numerous papers. From early in his career, Sylvan defended a sophisticated Meinong-inspired ontology, first presented in his 1966 paper, "Some Things Do Not Exist." After several more papers in the 1970s, the theory was given a book-length treatment in 1980, Exploring Meinong's Jungle and Beyond. The view—also defended in recent years by Priest—utilizes a modal theory including "impossible worlds" to deal with supposed objects, like the "round square." Sylvan's formulation is logically consistent, and avoids certain paradoxes associated with Meinong's original ontology; although, like many Meinongian views, it faces criticism due to its presumed ontological implausibility.
Outside of logic and metaphysics, Sylvan was a proponent of so-called deepenvironmental ethics in the study of environmental ethics. In his important 1973 paper "Is There a Need for a New, an Environmental, Ethic?", he defended a then-unorthodox account of the intrinsic value of the non-human, natural world. For this he was sometimes considered a defender of deep ecology, but he was in fact very critical of much of the domain. Beginning in the 1970s, Sylvan published several other notable articles and books on environmental ethics and issues, and he co-authored the 1994 book The Greening of Ethics with David Bennett. From his work in environmental ethics, Sylvan took an interest in anarchism, contributing an often-cited entry on the subject to A Companion to Contemporary Political Philosophy.