?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=The+Liar+and+Related+Paradoxes%3AFuzzy+Truth+Value+Assignment+for+Collections+of+Self-Referential+Sentences&rft.creator=Vezerides%2C+Kostis&rft.creator=Kehagias%2C+Dr.+Athanasios&rft.subject=Cognitive+Psychology&rft.subject=Logic&rft.description=We+study+self-referential+sentences+of+the+type+related+to+the+Liar+paradox.+In+particular%2C+we+consider+the+problem+of+assigning+consistent+fuzzy+truth+values+to+collections+of+self-referential+sentences.+We+show+that+the+problem+can+be+reduced+to+the+solution+of+a+system+of+nonlinear+equations.%0AFurthermore%2C+we+prove+that%2C+under+mild+conditions%2C+such+a+system+always+has+a+solution+(i.e.+a+consistent+truth+value+assignment)+and+that%2C+for+a+particular+implementation+of+logical+%60%60and''%2C+%60%60or''+and+%60%60negation''%2C+the+%60%60mid-point''%0Asolution+is+always+consistent.+Next+we+turn+to+computational+issues+and+present+several+truth-value+assignment+algorithms%3B+we+argue+that+these+algorithms+can++be+understood+as+generalized+sequential+reasoning.+In+an+Appendix+we+present+a+large+number+of+examples+of+self-referential+collections+(including+the+Liar+and+the+strengthened+Liar)%2C+we+formulate+the+corresponding+truth+value+equations+and+solve+them+analytically+and%2F+or+numerically.&rft.date=2003-09&rft.type=Preprint&rft.type=NonPeerReviewed&rft.format=application%2Fpostscript&rft.identifier=http%3A%2F%2Fcogprints.org%2F3171%2F1%2FFL1025.ps&rft.identifier=++Vezerides%2C+Kostis+and+Kehagias%2C+Dr.+Athanasios++(2003)+The+Liar+and+Related+Paradoxes%3AFuzzy+Truth+Value+Assignment+for+Collections+of+Self-Referential+Sentences.++%5BPreprint%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F3171%2F