\begin{frame}{Jan's Chess Playing Sisters} The sentence: \begin{scenter} \sentence{Apart from Mary, Jan has other sisters who play chess} \end{scenter} may have two readings: \begin{itemize} \pause \item \ldots\ \sentence{has at least one other sister} \ldots \pause \item \ldots\ \sentence{at least two other sisters} \ldots \end{itemize} \pause\medskip \begin{block}{\sentence{\ldots\ has at least one other sister \ldots}} \pause \begin{malign} \formula{ \binpred{S}{\const{m}}{\const{j}} \logandinf \unpred{C}{\const{m}} \logandinf \existsst{x}{\big(\, \notequalto{x}{\const{m}} \logandinf \binpred{S}{x}{\const{j}} \logandinf \unpred{C}{x} \,\big)}} \end{malign} \end{block} \pause\medskip \begin{block}{\sentence{\ldots\ at least two other sisters \ldots}} \pause \begin{malign} \binpred{S}{\const{m}}{\const{j}} \logandinf \unpred{C}{\const{m}} \logandinf \existsst{x}{\existsst{y}{\:\big(\, &\notequalto{x}{\const{m}} \logandinf \notequalto{y}{\const{m}} \logandinf \notequalto{x}{y}}} \\ &\logandinf \binpred{S}{x}{\const{j}} \logandinf \unpred{C}{x} \logandinf \binpred{S}{y}{\const{j}} \logandinf \unpred{C}{y} \,\big) \end{malign} \end{block} \end{frame} \theme{Natural Deduction with Equality}