Towards Recursive Models-A Computational Formalism for the Semantics of Temporal Presuppositions and Counterfactuals in Natural Language

syntax In order to analyze the above introduced phe nomena it is su cient to work on a restricted language fragment de ned in this section The usual way to formally de ne a fragment of the lan guage is to provide a grammar Since the consid ered phenomena occur in many natural languages almost every western language has the syntactic constructs necessary for expressing the previous utterances I prefer here a more abstract descrip tion to some extent independent from the partic ular language adopted I shall call such formalism abstract syntax The rst step to de ne the abstract syntax of the relevant natural language fragment that will be denoted with L is to specify a family of syntac tic functions functions that syntactically manip ulate sentences of the natural language to obtain other sentences The de nition of the abstract syntax of L is then obtained by means of a set hi erarchy starting from a set of simple sentences other sets containing complex and compound sen tences are obtained as the range of syntactic functions The union of these sets will be L The syntactic functions used to cover all the lin guistic phenomena presented in the previous sec tion are the following It is important to point out that future refers to the point of reference not to the point of speech In ut terance both the events happened in the past met and left but the second is in the future of the point of reference neg s returns the negation of sentence s For example if s is Mary left sentences are enclosed in single quotes neg s is Mary did not leave before s s returns the complex sentence formed by the main clause s and the tem poral subordinate s introduced by before Observe that the syntactic functions do not only concatenate the strings given as argu ments but also syntactically manipulate them to obtain the correct result For ex ample from Mary met John and Mary left using the syntactic function before one should obtain Mary met John before she left and not Mary met John before Mary left after s s returns the complex sentence formed by the main clause s and the tem poral subordinate s introduced by after and s s returns the compound sentence constituted by the two sentences s and s joined by the conjunction and nevertheless s s returns the compound sentence constituted by the two sentences s and s joined by the conjunction neverthe less Usually nevertheless s s is a pair of sentences separated by a full stop Here this detail is not important in that the two sentences from a semantic point of view are co ordinated cf s s returns the counterfactual sen tence with s as antecedent and s as con sequent For example if s is Mary met John and s is Mary left cf neg s s is If Mary had not met John she would have left wcf s s returns the weak counterfactual i e a sentence syntactically di ering from a counterfactual one in that even if substi tutes if For instance if s and s are the two sentences just met for the cf function then wcf neg s s is Even if Mary had not met John she would have left Now the syntactic functions listed above are used to formally de ne the fragment L as it was said before a set hierarchy is built the last set Informatica S Mizzaro before + after and + nevertheless