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More precisely, we characterize K45(<jats:bold>G<\/jats:bold>) as the set of valid formulae of the class of possibilistic G\u00f6del frames <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\langle W, \\pi \\rangle $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>\u27e8<\/mml:mo>\n                    <mml:mi>W<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>\u03c0<\/mml:mi>\n                    <mml:mo>\u27e9<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, where <jats:italic>W<\/jats:italic> is a non-empty set of worlds and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\pi : W \\mathop {\\rightarrow }[0,1]$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03c0<\/mml:mi>\n                    <mml:mo>:<\/mml:mo>\n                    <mml:mi>W<\/mml:mi>\n                    <mml:mo>\u2192<\/mml:mo>\n                    <mml:mo>[<\/mml:mo>\n                    <mml:mn>0<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>]<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is a possibility distribution on <jats:italic>W<\/jats:italic>. We provide decidability results as well. Moreover, we show that all the results also apply to the extension of K45(<jats:bold>G<\/jats:bold>) with the axiom (D), provided that we restrict ourselves to normalised G\u00f6del Kripke frames, i.e. frames <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\langle W, \\pi \\rangle $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>\u27e8<\/mml:mo>\n                    <mml:mi>W<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>\u03c0<\/mml:mi>\n                    <mml:mo>\u27e9<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> where <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\pi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c0<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> satisfies the normalisation condition <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\sup _{w \\in W} \\pi (w) = 1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msub>\n                      <mml:mo>sup<\/mml:mo>\n                      <mml:mrow>\n                        <mml:mi>w<\/mml:mi>\n                        <mml:mo>\u2208<\/mml:mo>\n                        <mml:mi>W<\/mml:mi>\n                      <\/mml:mrow>\n                    <\/mml:msub>\n                    <mml:mi>\u03c0<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>w<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s11225-022-09987-0","type":"journal-article","created":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T20:02:36Z","timestamp":1649448156000},"page":"1081-1114","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Simplified Kripke Semantics for K45-Like G\u00f6del Modal Logics and Its Axiomatic Extensions"],"prefix":"10.1007","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7551-2877","authenticated-orcid":false,"given":"Ricardo Oscar","family":"Rodriguez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Olim Frits","family":"Tuyt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4466-3298","authenticated-orcid":false,"given":"Francesc","family":"Esteva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6929-3126","authenticated-orcid":false,"given":"Llu\u00eds","family":"Godo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,8]]},"reference":[{"issue":"5","key":"9987_CR1","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1093\/logcom\/exp062","volume":"21","author":"F Bou","year":"2011","unstructured":"Bou, F., F. 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