2.2.2 In formal semantics
There are various approaches in the domain of semantics such as philosophical semantics(e.g.,Russel,1945),formal semantics(e.g.,Davidson,1980,1984),model theoretical semantics(e.g.,Montague,1974),cognitive semantics(e.g.,Talmy,1978;Fauconnier,1985),computational semantics(e.g.,Eijck & Unger,2010),etc.Formal semantics,just as Saeed(1997:270)proposes,is“one of the most important and liveliest in the semantics literature”.From the perspective of formal semantics,conjunctive resources are considered as the truth-functional connectives in propositional logic.The truth value of a connective is built on the truth value the propositions that it connects.Thus,conjunctions in formal semantics are usually called logical conjunctives or truth-functional connectives(e.g.,van Dijk,1978,van Wijk,2006,).
In semantic logic,logical connectives can conjoin two propositions which are either true or false.According to Saeed(1997:82),in the logical form,lower case letters such as p,q,r represent propositions or statements and the typical symbols representing the truth value of the connectives are:^for agreement(e.g.,and),¬for negation(e.g.,but),ˇfor choice(e.g.,or),→for material implication(e.g.,then),and≡for biconditional(e.g.,if...and only if).If these logical connectives conjoin two propositions or statements,there will be four cases referring to the truth value:(1)both p and q are true;(2)both p and q are false;(3).p is true but q is false and(4).p is false but q is true.
Davies(1979)mainly discusses the conditional conjunctions and causal conjunctions and divides the conditionals into four types:telling conditionals,decision conditionals,knowledge conditionals and performance conditionals.By analyzing the conditionals,Davies(1979:67)chiefly focuses on the occurrence value[1],i.e.“the happening of an event(/state of affairs)in extra-linguistic reality”of the main clause and subordinate clause.The ultimate aim is still to analyze the truth functional logic.These general types of conditional conjunctions can be generalized in Figure 2.3.
Figure 2.3 General types of conditional conjunctions(Based on Davies,1979:146-169)
Seen from Figure 2.3,the syntactical constructions in telling conditionals express“the reason for the full telling(saying)of the main clause”(Davies,1979:146).The antecedent clause in a telling condition presents a stage in a chain of thought which the speaker feels that another might not follow if it were not made explicit.As to the decision conditionals,Davies(1979:149)proposes that all the constructions realize a decision feature in their main clause.Knowledge conditionals are explicitly marked to show the deductive conclusion for knowledge is arrived at only by reasoning(Davies,1979:162).Moreover,performance conditionals are divided into three types:open prediction,induction and counterfactual constructions.
Being similar to the model of conditional conjunctions,the semantic model of reason is also separated into four types:reason for telling,reason for decision,reason for occurrence,and reason for knowledge.
Figure 2.4 General types of causal conjunction(Based on Davies,1979:169-176)
In Davies’s(1979:169)illustration,reason for telling signals some justification for saying the other clause.They are alone among constructions of explanation.Reason for decision presents“a given occurrence value in one clause,as a sufficient reason for making a decision concerning the performance of the event in the other”(Davies,1979:170).Constructions of motivation and constructions of purpose are two types in the relation of reason for decision.According to Davies(1979:173-174),reason for occurrence realises full independent knowledge of the event in the dependent clause,and the constructions of reason for knowledge“represent the fully closed counterparts of deductive conditionals”.
Based on the above illustrations,it can be seen that formal semantics translate a natural language such as English into a kind of logical language,with which we can translate one language to another.The truth of the proposition and the reasonability of the logic are the focus in this approach.For example,scholars such as Partee(1982),Dowthy(1980)and Cooper(1979)show how the generalized conjunction schema makes some correct predictions and some wrong ones.
All in all,the perspective of formal semantics mainly concerns the truth logic of the proposition.The economy and formality of the traditional disciplines of logic are transformed into linguistics and logicians and linguists can make explicit between the connectives and the propositions or statements they connect.However,these connectives are not pragmatically appropriate and it is necessary to present some pragmatic-communicative explanation about these logical connectives.
In China,the researches of conjunctives in formal semantics are mainly in the form of general review(e.g.,李可胜,2009;代尊峰,孙洪波,2014).Jia et al.(贾改琴,邹崇理,2009)use the theories of formal semantics to analyze Chinese syntax,including conjunctive resources.