Počet záznamov: 1
Expanding Belnap: dualities for a new class of default bilattices
SYS 0287435 LBL 02711^^^^^2200265^^^450 005 20240104141030.4 014 $a 000567500100001 $2 WOS CC. SCIE 014 $a 000567500100001 $2 CCC 014 $a 2-s2.0-85090889289 $2 SCOPUS 017 70
$a 10.1007/s00012-020-00678-2 $2 DOI 035 $a biblio/213606 $2 CREPC2 100 $a 20200914d2020 m y slo 03 ba 101 0-
$a eng 102 $a CH 200 1-
$a Expanding Belnap: dualities for a new class of default bilattices $f Andrew P. K. Craig, Brian A. Davey, Miroslav Haviar 330 0-
$a Bilattices provide an algebraic tool with which to model simultaneously knowledge and truth. They were introduced by Belnap in 1977 in a paper entitled How a computer should think. Belnap argued that instead of using a logic with two values, for ‘true’ and ‘false’, a computer should use a logic with two further values, for ‘contradiction’ and ‘no information´. The resulting structure is equipped with two lattice orders, a knowledge order and a truth order, and hence is called a bilattice. Prioritised default bilattices include not only values for ‘true’, ‘false’, ‘contradiction’ and ‘no information’, but also indexed families of default values for simultaneous modelling of degrees of knowledge and truth. We focus on a new family of prioritised default bilattices: Jn, for all natural numbers n. The bilattice J0 is precisely Belnap’s seminal example. We obtain a multisorted duality for the variety generated by Jn, and separately a single sorted duality for the quasivariety generated by Jn. The main tool for both dualities is a unified approach that enables us to identify the meet-irreducible elements of the appropriate subuniverse lattices. Our results provide an interesting example where the multi-sorted duality for the variety has a simpler structure than the single-sorted duality for the quasivariety 463 -1
$1 001 umb_un_cat*0289131 $1 011 $a 0002-5240 $1 011 $a 1420-8911 $1 200 1 $a Algebra universalis $v Vol. 81, no. 4 (2020), pp. 1-26 $1 210 $a Basel $c Springer Nature Switzerland AG $d 2020 606 0-
$3 umb_un_auth*0125164 $a natural duality 606 0-
$3 umb_un_auth*0052636 $a výsledky $X results 606 0-
$3 umb_un_auth*0117329 $a algebras 608 $3 umb_un_auth*0273282 $a články $X journal articles 700 -1
$3 umb_un_auth*0226852 $a Craig $b Andrew, P. K. $4 070 $9 34 701 -0
$3 umb_un_auth*0003450 $a Davey $b Brian A. $4 070 $9 33 701 -0
$3 umb_un_auth*0002686 $a Haviar $b Miroslav $p UMBFP10 $4 070 $9 33 $f 1965- $T Katedra matematiky 801 $a SK $b BB301 $g AACR2 $9 unimarc sk 856 $u https://link.springer.com/journal/12/volumes-and-issues/81-4 $a Link na zdrojový dokument T85 $x existuji fulltexy
Počet záznamov: 1