The nth power of an operator is defined to mean applying the operator n times in succession . 一個(gè)算符的n次冪定義為連續(xù)運(yùn)用算符n次。
Based on lattice - valued propositional logic system lp ( x ) and lattice - valued first - order logic system lf ( x ) , the author studied semantic and syntax properties of generalized lattice - valued modal logic system , and probed into a - resolution principle . the specific contents are as follows : part one the study of lattice - valued modal propositional logic system and its resolution method in this part , we introduced modal operators n ( necessary ) and p ( possible ) into lattice - valued propositional logic system lp ( x ) , set up a new lattice - valued modal propositional logic system lmp ( x ) , studied its semantic properties and syntax structure , proved the soundness and consistence of this system . based on these work , discussed a - resolution principle of lattice - valued modal propositional logic system lmp ( x ) , gave out the rules of computing a - direct resolvent and a - self resolvent , and proposed detailed resolution method 本文在格值命題邏輯系統(tǒng)lp ( x )和格值一階邏輯系統(tǒng)lf ( x )的基礎(chǔ)上,討論了廣義格值模態(tài)邏輯系統(tǒng)的語(yǔ)義及語(yǔ)法性質(zhì),并對(duì)其-歸結(jié)原理做了初步探討,主要在下述三個(gè)方面取得了研究成果:第一部分:關(guān)于格值模態(tài)命題邏輯系統(tǒng)及其歸結(jié)方法的研究在此部分,把模態(tài)算子n (必然)和p (可能)引入格值命題邏輯系統(tǒng)lp ( x ) ,建立了新的格值模態(tài)命題邏輯系統(tǒng)lmp ( x ) ,并研究了它的語(yǔ)義刻畫(huà)及語(yǔ)法結(jié)構(gòu),證明了在此語(yǔ)義解釋和語(yǔ)法框架下的系統(tǒng)仍是-可靠的和協(xié)調(diào)的;在此基礎(chǔ)上,進(jìn)一步研究了基于格值模態(tài)命題邏輯系統(tǒng)lmp ( x )的-歸結(jié)原理,給出了計(jì)算-直接歸結(jié)式和-自歸結(jié)式的規(guī)則,并總結(jié)出具體的歸結(jié)方法。