Speaker
Antonio Piccolomini d'Aragona
University of Siena
Talks at this conference:
Friday, 18:10, J335 
Inversion in nonmonotonic PTS 
Prawitzâ€™s prooftheoretic semantics evaluates validity of proofs \(\models^{\texttt{P}}\) over atomic bases \(\mathfrak{B}\) and detour reductions. In current approaches, proofs and reductions are left out, and consequence \(\models\) is defined outright; a variant \(\models^{\texttt{S}}\), due to Sandqvist, deals with disjunction in an eliminationlike way. \(\models^{\texttt{P}}\), \(\models\) and \(\models^{\texttt{S}}\) can be given in a monotonic or nonmonotonic format, according to whether extensions of \(\mathfrak{B}\) are brought in when defining, by closure, consequence under assumptions. Completeness results have been proved on nonmonotonic and monotonic \(\models\), and monotonic \(\models^{\texttt{S}}\) [2]. In the monotonic framework, these results adapt to \(\models^{\texttt{P}}\) modulo conditions for equivalence and completeness on \(\models^{\texttt{P}}\) [1]. I show that similar results hold in the nonmonotonic approach too, via the following:
1 also holds with classical metalogic and a strict \(\models^{\texttt{P}}\) where closure is necessary but not sufficient for validity when \(\Gamma \neq \emptyset\). 3 also holds with \(\models\) and strict \(\models^{\texttt{P}}\). Bibliography
