Purely Syntactic Methods

  • Francesca PoggiolesiEmail author
Part of the Trends in Logic book series (TREN, volume 32)


In the early 1980s, the failures of the search for a sequent calculus for modal logic gave rise to the idea that the standard Gentzen calculus could only account for classical and intuitionistic logics and should therefore be enriched. Logicians thus started creating methods capable of generating extensions of the sequent calculus and hence suitable for providing modal logic, as well as other logics, with computational tools. These methods can be divided into two groups: the first group consists of methods that generate purely syntactic sequent calculi, while the second group include methods that extend the standard sequent calculus by adding explicit semantic elements. In this chapter we present and discuss the main calculi belonging to the first group.


Modal Logic Structural Connective Logical Rule Sequent Calculus Frame Property 
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