Reasoning with Time Intervals: A Logical and Computational Perspective

<table>Hasse diagram of fragments of <svg height="15.8375" id="M428" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 43.299999 15.8375" width="43.299999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,15.775)"><path d="M346 674l289 -674h-96l-82 200h-249l-81 -200h-96l289 674h26zM239 274h188l-94 229z" id="x1D5A0"></path></g>
<g transform="matrix(1.25,0,0,-1.25,90,90)">
<path d="m -62.89,70.93 9.05,0" style="fill:none;stroke:#000000;stroke-width:0.68000001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<g transform="matrix(.017,0,0,-.017,11.388,15.775)"><path d="M346 674l289 -674h-96l-82 200h-249l-81 -200h-96l289 674h26zM239 274h188l-94 229z" id="x1D5A0"></path></g><g transform="matrix(.017,0,0,-.017,22.709,15.775)"><path d="M74 0v662h205q232 0 232 -163q0 -91 -92 -133q128 -41 128 -173q0 -52 -29 -97t-77 -70q-54 -26 -127 -26h-240zM161 588v-194h90q88 0 129.5 25.5t41.5 79.5q0 46 -31.5 67.5t-99.5 21.5h-130zM161 317v-243h126q84 0 127.5 34.5t43.5 93.5q0 36 -19.5 63.5t-53.5 38.5
q-39 13 -145 13h-79z" id="x1D5A1"></path></g>
<g transform="matrix(1.25,0,0,-1.25,90,90)">
<path d="m -45.62,70.77 8.21,0" style="fill:none;stroke:#000000;stroke-width:0.68000001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<g transform="matrix(.017,0,0,-.017,32.975,15.775)"><path d="M74 0v662h205q232 0 232 -163q0 -91 -92 -133q128 -41 128 -173q0 -52 -29 -97t-77 -70q-54 -26 -127 -26h-240zM161 588v-194h90q88 0 129.5 25.5t41.5 79.5q0 46 -31.5 67.5t-99.5 21.5h-130zM161 317v-243h126q84 0 127.5 34.5t43.5 93.5q0 36 -19.5 63.5t-53.5 38.5
q-39 13 -145 13h-79z" id="x1D5A1"></path></g>
</svg> and <svg height="15.8375" id="M429" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 42.587502 15.8375" width="42.587502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,15.775)"><path d="M346 674l289 -674h-96l-82 200h-249l-81 -200h-96l289 674h26zM239 274h188l-94 229z" id="x1D5A0"></path></g>
<g transform="matrix(1.25,0,0,-1.25,90,90)">
<path d="m -62.89,70.93 9.05,0" style="fill:none;stroke:#000000;stroke-width:0.68000001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<g transform="matrix(.017,0,0,-.017,11.388,15.775)"><path d="M346 674l289 -674h-96l-82 200h-249l-81 -200h-96l289 674h26zM239 274h188l-94 229z" id="x1D5A0"></path></g><g transform="matrix(.017,0,0,-.017,22.709,15.775)"><path d="M161 74h379l-17 -74h-449v662h439v-74h-352v-202h305v-75h-305v-237z" id="x1D5A4"></path></g>
<g transform="matrix(1.25,0,0,-1.25,90,90)">
<path d="m -45.91,70.77 7.93,0" style="fill:none;stroke:#000000;stroke-width:0.68000001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<g transform="matrix(.017,0,0,-.017,32.613,15.775)"><path d="M161 74h379l-17 -74h-449v662h439v-74h-352v-202h305v-75h-305v-237z" id="x1D5A4"></path></g>
</svg> over strongly discrete linear orders.</table>

International Scholarly Research Notices

fig5

Figure 5

Figure 5: Reasoning with Time Intervals: A Logical and Computational Perspective 