The problems \(\sc{SATISFIABILITY}_{\mathcal{L}}\), \(\sc{VALIDITY}_{\mathcal{L}}\), and \(\sc{MODEL}\ \sc{CHECKING}_{\mathcal{L}}\) have been studied for many of the logics employed in philosophy, computer science, and artificial intelligence. A number of results are summarized in Table 1, focusing on systems surveyed in other articles in this encyclopedia. The reader is referred to these and the other references provided for the definition of the fragment or system in question as well as the relevant definitions of \(\mathfrak{A}\), \(\models_{\mathcal{L}}\), or \(\vdash_{\Gamma_{\mathcal{L}}}\).[42]