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<?xml version="1.0" standalone="yes"?> <Paper uid="E91-1045"> <Title>HELPFUL ANSWERS TO MODAL AND tlYPOTHETICAL QUESTIONS</Title> <Section position="4" start_page="0" end_page="0" type="metho"> <SectionTitle> 3.0 IIELPFULNESS, MEDALS AND QUESTIONS </SectionTitle> <Paragraph position="0"> Though tile problem of helpfully answering modal questions touches on many issues, four particular points need to be ad, dressed.</Paragraph> <Section position="1" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.1 Modality. </SectionTitle> <Paragraph position="0"> When looking at the example set out in the introduction, the question arises whether the range of &quot;correct&quot; answers to some extent corresponds to ambiguity (ability/possibility) residing in the ,nodal can. Indeed, a large proportion of the literature on modality concerns the view that medals are polysemous, depending on the kind and degree of modality they express (epistemic, deon.</Paragraph> <Paragraph position="1"> tic, etc.) \[Palmer 1979, 1986; Quirk et at. 19851. Usually, attempts are made to identify modal &quot;primitives&quot; (ability, permission, etc) and 1o analyse modal constructs as ambiguous over several &quot;literal&quot; meanings involving these primitives. Invariably, polysemie reduetionist approaches to modal constructs run into problems: given any classification of core types of modality, it is often hnpossible to determine which reading is involved in any particular example \[Coates 1983 versus Walton 1988\].</Paragraph> <Paragraph position="2"> Kratzer \[19771 lakes another view. She presents a unified anal, ysis of modality which includes the treatment of conditionals (and hence hypotheticals). Medals are unarubiguous and modal constructs are analysed as tri-partite structures lsee also Partee 1988, Heinz 1982\], comprising a ,nodal operator, a conversational background, and a proposition. For example, ill \[Kratzer 1977\] the modal mu..yC/ in the following sentences: (at All Maori children must learn the names of their aucestol~.</Paragraph> <Paragraph position="3"> (b) The ancestors of the Maoris must have arrived from Tahiti.</Paragraph> <Paragraph position="4"> (c) If you must sneeze, at least use your handkerchief.</Paragraph> <Paragraph position="5"> (d) When Kahukura-uui (lied, the people of Kahungunu said: Rakaipaka must be our chief.</Paragraph> <Paragraph position="6"> is traditionally analysed as (at 'deontic' must indicating duty, (b) 'epistemic' must referring to a piece of knowledge or informa null tion, (c) 'dispositional' must, referring to people's dispositions (e.g. they cannot help sneezing), and (d) 'preferential' must referring to preferences and wishes. Kratzer points out that classifications of medals drawn in the polysemy paradigms never adequately cover the data and that new examples are easily found to demonstrate the need for ever more refined categories of modal meaning.</Paragraph> <Paragraph position="7"> Kratzer wishes to propose a treatment that brings out the common factor in all uses of mu~C/ (and of other medals) and suggests that the burden of differentiation is to be placed on a variation in - 257 context. As such, tile meaning of (a)-(d) entertains a relationship with the meaning of (a')-(d') resl~ectively: (a) In view of what their tribal duties are, all Maori children nlust learn the names of their ancestors.</Paragraph> <Paragraph position="8"> (b) In view of what is known, the ancestors of the Maoris must have arrived from Talfiti.</Paragraph> <Paragraph position="9"> (c) If, in view of what your dispositions are, you must sneeze, at least use your handkerchief.</Paragraph> <Paragraph position="10"> (d) When Kahukura-nui died, the people of Kahungutm said: In view of what is good for us, Rakaip',dr, a must 1~ our chief.</Paragraph> <Paragraph position="11"> and she defines the sematic interpretation underlying mt~al constructs as a tripartite structure (applied to (b)): Sentence: Operator: Must in view of First Argumeut: What is known Second Argument: The ancestors of the Maori have arrived fi'om Tahiti.</Paragraph> <Paragraph position="12"> The modal is an operator which takes a context and a proposition. The Intth conditions for t/!C/~st, interpreted as necessity, dictate that the modal construct is true if the proposition (the second argument) logically follows from the context (the first argument). A similar approach to can (possibility) unpacks its truth conditions as true if the context (the first argument) is logically compatible:(i.e, does not induce a contradiction) with the prgposition (the second argument). Kratzer works within the classical possible world tradition. Conversational backgrounds, modelled' as sets of propositions, are usually itoplicit and linked to tile utterance situation, though it is not clear by what n~echanisru. : : Kratzer 119831 proceeds to distinguish between different kinds of conversational backgrounds, depending on the infornlation they contain. She does however experience difficulties when trying to identify different context classes. Indeed, it is as difficult to isolate different conversational backgrounds as it is to pinpoint tile various meanings a modal might have.</Paragraph> </Section> <Section position="2" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.2 Questions attd Answers </SectionTitle> <Paragraph position="0"> It is also necessary to present a coherent perspective on questions ~md answers. Groenendijk and Stockhof \[19841 compile an overview of various treatnaents of questions that populate tile field and investigate desiderata for a semantic tlteory. They arguethat interrogatives are entitled to a meaning of their own (and should not be viewed as, say, hidden imperatives) but that their treatment must show some equivalence with that of indirect questions. The meaning of a question is to be related inextricahly with its answerhood conditions. Groenendijk and Stockhof work in the possible world tradition and they cast the interpretation of a.qnestion as'a function which, for every index, returns its tree answer. Conskler the following example. The semantics givet~ to a question Does Peter walk? is a partition of the set of possible worhls into .two: those worlds where Peter walks, and those ~orlds where Peter does not walk. Both Peter walks and Peter does not walk are possible semantic answers to the question. Each possible world belongs to one or the other of these partitions, so each possible world offers only one true answer to the question. This analysis caters for entailment between questions (question Q entails question R if all true answers to Q are also true answers to R) and thus explains entailment between coordinated questions. Groenendijk mad Stockhof elaborate the basic treatment of yes/no questions; wh-questions are reduced to this basic type. They also provide an interpretation for constituent answers. They assume that modal questions will be analysed at some other pragmatic level.</Paragraph> <Paragraph position="1"> The work described constitutes tile :most extensive treatuzent of the semantics of questions aml answers to date. llowcver, in our view, it cannot be directly incorporated in a pragmatic!model, for two reasons. First of all, the semantic model assumes completeness of infonnation, and complete nmtual awareness of speakers' belief states (but then, wily ask questions of one another?). They do attempt to build, from this, an account of how to reason with partial knowledge but, as they work in a traditional extensional frmnework, this results in clashes with the semantic theory. (In short, what a person knows is a set of possible worlds, namely all those possible worlds that are consistent with his/her beliefs.</Paragraph> <Paragraph position="2"> The semantics of questions is given as a partition over all possible worlds, in an extensional framework - where intensions are derived from extensions - this means that if a person entertains partial beliefs, he/she cannot know the meaning of a question.) Secondly, there may be more than one true answer to a question, and all should be captured by Groenendijk and Stockhof's theory. But how are these answers defined, even computed, from the question7 And, as illustrated in the example given in the intro.</Paragraph> <Paragraph position="3"> duction, even if we know how to generate such answers, how do we define a helpful answer?</Paragraph> </Section> <Section position="3" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.3 Helpfulness </SectionTitle> <Paragraph position="0"> It is not easy to give a definition of a &quot;helpful&quot; answer off the cuff. Formal sere.antic theories have little to say on this issue, though some cognitively oriented frameworks have developed useful views.</Paragraph> <Paragraph position="1"> Relevance Theory {Sperber and Wilson 1986\] has given an account of context-sensitivity in cormnunication. It postulates that when people understand, they attempt to maximise relevance i.e. tbey pick the context against which the relevance of an utterance is greatest. Relevance, thus, is quantifiable and defined by means of extent conditions: an assumption is relevant in a con.</Paragraph> <Paragraph position="2"> text to the extent that its effects in this co,ltext are large and the effort to process \[t is smaU.</Paragraph> <Paragraph position="3"> it should be clear from the onset that the specification of Relevance Theory isnot precise enough to be implemented as it stands. There are, however, three principles which axe interesting for our purpc~/e. (i) The most relevant context for interpreting a question is that a Ye__a-answer is desired. This helps towards explaining why helpful answers are given at all, and why they occur typically with negative answezs. (ii) The selection of relevant contexts is eml~died in the human cognitive machinery and ensures that, an utterance receives only one interpretation (and not many from which a particular one is selected). Indeed, as shown in the introduction, there may be more than one true answer to a question but only one appropriate one, which must be characterized..(iii) The theory specifies that all contextual effects are explained against the background of assumptions which a person may hold and postulates mechanisms by means of which relevant contexts can be pinned down starting from situational information and the utterance itself.</Paragraph> </Section> <Section position="4" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.4 Context </SectionTitle> <Paragraph position="0"> The necessity to give a more precise definition of context becomes obvious from the previous sections. Questions can only be answered in context, medals seem to receive different interpretations according to varying contexts, and any cognitively appealing notion of &quot;helpfulness&quot; or &quot;relevance&quot; is stated in terms of contexts. All this ties in with current work in formal semantics which explores tri-partite structures (tying in context with propositional content of utterances) as a basic mechanism for semantic interpretation Illeim 1982, Partee 19881. However, though current formal semantic theory is steadily increasing the workload of context, its precise nature remains vague. It is not enough to furnish fonnal semantic interpretations &quot;relative&quot; to some context: a satisfactory approach to a formal but cognitively attractive characterization of &quot;helpful&quot; answers seems to war, rant a closer look at the content of conversational backgrounds, their relation to ihe utterance and its situation, and an appreciation of whether they can be computed.</Paragraph> <Paragraph position="1"> The insights offered by Relevance Theory may be compatible with fonnal (and computational) semantic theories, and offer a practical starting point when trying to pin down a fuller notion - 258 of context. In order to investigate this, we need to define our intuitions in an implementable fr,'unework. Please note that it is not our intention to attempt a foml.'disation or an implementation of Relevance Theory, but merely to define an experimental franlework capable of handling contexts in order to derive helpful answers to modal and hypothetical questions, alheit exploiting insights front Relevance Tlleory if possible.</Paragraph> </Section> </Section> <Section position="5" start_page="0" end_page="0" type="metho"> <SectionTitle> 4.0 TOWARDS A TilEORY OF PRAGMATICS </SectionTitle> <Paragraph position="0"> It is our intuition that, when people communicate, they know different things, or there woulkl be no point in communicating. Thus it seems that any realistic inodei of communication must allow for partiality in what agents know. Since agents retain inferential capabilities, we assume their beliefs are consistent. As a consequence,.</Paragraph> <Paragraph position="1"> our model represents agents as partial, consistent sets of propositions. The notion of proposition deployed is takon straight from Property Theory ITumer 1987, Chierchia el al 1989, see also Ramsay 19901, a weak first order theory with fine grained intensionality. null Questions are not themselves propositions; they are not associated with truth values. They do, however, entertain a relationship with propositions. In our view, a simple yes/no question embodies a proposition whose truth value is notknown to the agent asking the question. An answer to the question is any proposition which, if added to the agent's beliefs, will force truth or falsity of the proposition embodied in the question. This view on answerhood is much looser than the one adopted by Groenendijk and Stockhof in that it allows answers other than true semantic answers. Indeed, any answer will do as long as it allows all agent to conclude to the true seinantic answer. Thus, a question Does Peter walk? may be answered by Peter sleeps in this framework (and not just by either of Peter walks or Peter does not walk) as long as that information allows the agent to conclude that Peter walks or that Peter does not wal.k. This constrains the agent's reasoning capacity which nmst now deal with partial information. It also means that agents' beliefs must he subject to revision.</Paragraph> <Paragraph position="2"> In order to reflect these intuitions in our theory, we extended the language of Property Theory with a predicate which holds of questions, and an operator which, given a proposition, will yield a question. An axiomatisation governs conjunction of questions. A relation of answerhood is defined which holds between a question and its answer (a proposition). The behaviour of this relation is given through axiomatisation of a proof theory.</Paragraph> <Paragraph position="3"> We adopt a view on inodality parallel to Kratzer's: our working hypothesis states that modals are not ambiguous and that any difference in interpretation resides in contextual diversity. We do not, however, try to classify contexts; a hopeless task which is no different to attempting to classify modal mnbiguity. ~a.n and must correspond to the inodal operators of passibility and necessity. Modal constructs are analysed in terins of these operators, a context attd a proposition. A context is a collection of propositions, which is a cohsistent subset of the agent's total beliefs. Necessity is true if the negatiotl of the proposition causes a contradiction in the context; possibility is true if the proposition can be accolmnodated within the context without giving rise to a contradiction (i.e. the context can he updated with the proposition).</Paragraph> <Paragraph position="4"> Questions, whether they are simple or modal, are equally analysed as tri-partite structures COlnprising an operator, a context and a proposition. For simple yes/no questions file operator is the QuestionTruth predicate (which can he safely stated in Property Theory). For modal questions, tile operator is tile Question counterpart of the appropriate modal operator. As with Groenendijk and Stockhof, wh-questions are reduced to yes/no questions. It should follow from tile above that Groenendijk and Stockhof's results carry over into this model, as the notion of semantic answedtood is preserved (though in an extended franlework).</Paragraph> <Paragraph position="5"> Following Kratzer, conditionals are treated like modals but tim context is ulxlated with the antecedent. We are not, however, treating connterfactuals at this stage (i.e. we only treat cases where the context can be uixlated with the antecedent and wberC/ no contradictions occur as a result).</Paragraph> <Paragraph position="6"> fu defining &quot;helpfulness&quot;, we take the view of Relevance Theory that a positive answer to the proposition embedded in tim question is desirable. As such, yes-answers become uninterest, ing as they are already nmximally helpful. No-answers, on the other hand, where the proposition cannot be accommodated by the context, can be helpful if they indicate why the proposition is inconlpatible with a state of affairs, or how the state of altairs might change so that it can be updated with the proposition. In the theory, this information is available frum the logic underpinning the answerhood relation relativised to a context. However, this furnishes us with a semantics only. To arrive at some view of how this may interact with pragmatics, the content of contexts must be fleshed out.</Paragraph> <Paragraph position="7"> Intuition tells us that only one helpful answer is furnished per context. Following Kratzer, and Relevance Theory, we assume that the burden of being helpful and relevant rests with the nlechanism which defines the context for an utterance given a situation. Many factors may contribute to this mechanism and it seems reasonable that knowledge of the physical circumstances (i.e. speakers, time, location, etc.) should play a role. The utter, ance itself must also contribute. As the literature offers no de, tailed information on how io model tim relationship between context and utterance, we have developed an implementation of a context machine which, initially, derived context from lexical information. This hnplementation was changed and refined in order to attempt to determine experhnenlally what the requiremerits for a &quot;context machine&quot; Inay be.</Paragraph> </Section> <Section position="6" start_page="0" end_page="0" type="metho"> <SectionTitle> 5.0 TIlE IMPLEMENTATION </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 5.1 The Overali Framework </SectionTitle> <Paragraph position="0"> The implementation of the overall framework consists of a parser, a knowledge base, a context machine and a theorem prover. The knowledge base, a consistent collection of proposi.</Paragraph> <Paragraph position="1"> lions, is set up to represent the beliefs of an agent who is to answer questions. For convenience of computation, the items in it are cast as sorted property-theoretic expressions (a sortal hierarchy can he achieved without sorting quantified variables - sorting and closing the world with respect to individuals merely has the effect of rendering the ilnplementation of the first order language decidable), Each knowledge base item is tagged with keys linking the information it contains with words in the lexiCOll. null The parser, a bi-directional chart parser \[Steel and De Reeck 19871 augmented with feature structures, works from an essem dally context free rule base where semantic translation rules ar c pair~! up with tim syntactic statement. The semantic representation delivered by the parser is an expression in Property Theory capturing the structural aspects of question's meaning.</Paragraph> <Paragraph position="2"> This Property-Tbeoretic expression is passed to the context, machine. It yields, from the Property-Theoretic expression, a tri-partite structure comprising an operator, a context and a proposition derived from the question. The role of the context machine is to extract from the knowledge base that information which is relevant to finding a helpful answer to the question.</Paragraph> <Paragraph position="3"> The proposition delivered by the context machine is given in the language of the logic K-T IOheid 1990\]. K-T is a propositional, non-monotonic logic which employs Kleene's strong three-valued colmectives, aqd which is extended with two modal operators (the language can he propositional as the knowledge base is sorted and closed). The semantics of the logic arC/~ expressed in terms of states of partial information which allow an agent to he uncertain about the truth or falsity of his knowl- 259 edge, and where possible, to make assumptions on the basis of what is not known to be false. The infereoce rules of K-T are given in the Appemlix.</Paragraph> <Paragraph position="4"> The propositional content of the input question is set against a suitable subset of the agent's knowledge, i.e. the context. The theorem prover then attempts to prove in the system K-T that the propositional content of the input question follows from the context. This it might achieve monotonically; or non-monotonically with the aid of assumptions, it is the record left in the wake of the proof process in each case, which we interpret in order to provide a helpful answer.</Paragraph> </Section> <Section position="2" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 5.2 The Theorem Prover. </SectionTitle> <Paragraph position="0"> The theorem prover is a three valued, modal analogue of a semantic tableau theorem prover \[Beth 1962; Jeffrey 19671. This method perfonns a case-wise analysis of all models in which the premises (read context) might be true while contradicting the conclusion (read propositional conteqt of the inpu\[ question), if no such models are found to exist, the theorem is proven. We employ this method because it allows a user absolute access to every stage of the proof process. We then exploit this access in order to find a helpful answer. If a proof succeeds monotonically, the agent's answer is sunply Yes. If it succeeds by means of one or more assumptions, the answer is of the fonn Yes, if .... where the body of tile/f-clause is the infonnation that was assulned. Where a proof fails, we have the task of detennining the reason why it failad - i.e. which assumptions shouhl be made to yield a y._e.~-answer. The proof process constructs a tree of which the branches represeot individual models. These models are closely or distantly related to one =mother according to how much of the proof tree they have in conunon. A failed proof has one or more models which are consistent, a,ld therefore counterexamples to our intended inference. We are able to compare these consistent models with closely related inconsistent ones. We can theo identify the contradiction which is in some sense missing. - i.e. we point to the particular premise or premises which are too weak to support the inference. A helpful answer in this case takes the form No, unless ... and the body of the unlessclause is composed of the strengthening required in a premise or premises so that the counterexampleswould no longer arise. This method remains constant regardless Of the actual content of the context. Note that a single answer is always yielded and that the borden of assuring that its content is &quot;helpful&quot; rests entirely on the context machine.</Paragraph> </Section> <Section position="3" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 5.3 The Context Machine. </SectionTitle> <Paragraph position="0"> Different inlplemeotations of the context selection mechanism have been attempted. Originally. it 6perat.ed by intersecting that part of the knowledge base which concerns the individuals and relations mentioned in the utterance. In this sense, it relied exclusively on lexical information as the process operated by selecting propositions associated with lexicai items reflected as objects in the knowledge base. It used closure on the sortal hierarchy to achieve this. This approach is compatible with Relevance Theory as it can be argued that Encyclopedic IOiowledge can be thus implemented.</Paragraph> <Paragraph position="1"> A side effect is lexical dismnbiguation - different readings of a word are associated with different clusters of information; only compatible infonnation will survive the intersection.</Paragraph> <Paragraph position="2"> This version was tested on a knowledge base modelling a building site, containing information about, buildings, workers, materials and time tables. The domain proved too complex to allow for any conclusions to be drawn: the diversity of objects whose behaviour needed modelling (including some beyond tile current state of the art - e.g.. mass vs count objects, plurals, time and teose, etc.) was prohibitive. Two other domains were tackled as a consequence: marital relationships and law, and the simple situation of what it takes to drive a car.</Paragraph> <Paragraph position="3"> Eveo against simple domains, it became clear that mere relia~lce on keying lexical infonnatiou would not be sufficient. The search space remahled large and insufficiently focussed as it included propositions which never contributed to deriving an answer, and a closer interaction between context machine and proof process should be postulated. It seems that tile context selection mechanism must have a model of inference. An attempt at such a mechanism was developed.</Paragraph> <Paragraph position="4"> The cootext machine Mark II extracts from the knowledge base any information which enable the truth of the proposition associated with tile question to be derived. Any implication in the knowledge base with that proposition as a consequent is selected to form part of the context and all rules and assertions which enable the truth of the antecedent of the hnplication to be derived axe also included. Any other rules, which cannot impinge upon the truth of the goal clause, are omitted as they are 'irrelevant' to the proof. In a sense, this selection process anticipates the structure of the proof itself. In the full system, the instantiation of quantified variables in sentences extracted from the knowledge base, is restricted to those individuals mentioned in the question, or relevant to those assertions made about individuals mentioned in the question. This is implemented using the sortal hierarchy. The examples given in Section 5 are derived using this version over a very restricted domain.</Paragraph> <Paragraph position="5"> Though the results were more satisfactory, the contexts derived in complex domains are still large. Though all information selected plays a part in the overall proof, the search space is unifonn for each proof branch. It became clear that a full interac.</Paragraph> <Paragraph position="6"> tioo between the structure of the proof and context selection nmst be achieved. A third version of the context machine attempted to derive contexts local to particular steps in the proof process. Though incomplete, the experience gained in the at, tmnpt convinced us that the selection of 'relevant' contextual information is dynamic, hffonnation pertaining to particular steps in the derivation of all aqswer should be local to that step and differeot 'relevant' contexts should be made accessible as the derivatiou progresses.</Paragraph> </Section> </Section> <Section position="7" start_page="0" end_page="0" type="metho"> <SectionTitle> 6.0 AN EXAMPLE </SectionTitle> <Paragraph position="0"> This sectioo elaborates an exanlple to illustrate (i) the basic theorem prover and (ii) the behaviour of context machines. To sinlplify the examples, we consider the case where there is only one individual, Anne. The set up coocerus finding a helpful answer to Cm~ Antic drive? First we present a successful proof, working from an optimal context which yields that Anne can indeed drive. The rules to tile theorem prover (K-T IObeid 1988\]) are given in the Appendix. Notice that premises are theorems of the logic and so any premise of form ~ is logically equivalent to The theorem prover reports that the inference KB I- drive(a) is proven by refutation. This we know because each path is inconsistent. The inference was proven monotonically (there was no need for assumptions) and required no sub-proof. The answer here is Ye___ss: Anne can drive because she has a lieence, she owns a ear and she has tile required skills.</Paragraph> <Paragraph position="1"> In the second example, the premise that Anne has a licence is removed. The proof fails to show monotonically that Anne eaq drive. &quot;llae system therefore ,sets out to assume that Anne might have a licence and thus attempts to fill the gap in the agent's in- null In this case, if we can assume the premise M licenced(a) successfully, we can prove tile original assertion monotonically. In this context there are no fonnulae which might affect the truth of M licenced(a) so our proof succeeds trivially. The answer here is Yes, i\[ Anne has a licence. In the next exmnple, we add explicitly that Anne does not have a licence. We assume that this infomlation is known and does not need a sub-proof.</Paragraph> <Paragraph position="2"> Again, the proof fails monotonically as in the second example.</Paragraph> <Paragraph position="3"> An attempt to hold an assumption that Anne has a licence will, IIowever, fail as it will contradict the premise \[3\] which states that such an assumption is false. The answer in this case is No, because Antle doe~ not Ilave a licenfe.</Paragraph> <Paragraph position="4"> The procedure for dealing with hypotheticals is similar but the context is updated with the antecedent before the proof of the consequent is carried out. Counterfactuals, which would require total revision of the knowledge base, are not treated.</Paragraph> <Paragraph position="5"> We can use these examples to illustrate the problems faced with selecting the appropriate contexts to yield helpful answers. The earliest version of the context machine would have selected all infonnation associated with domain objects directly related to the words in the sentence (Anne and driving), and all information associated with the sortal hierarchy involving those objects. The union of all these propositions produced a context that was not adequate: only some properties of Anne will affect hdr driving, and not all knowledge about vehicles will contribute to finding an answer to whether Anne can drive. Itatersection of clusters of information obtained by closure on tile hierarchy has tile side effect of achieving lexical disambiguation, but, in complex domains, it excluded some relevant facts from the context, whilst still including propositions which could never play a role in the proof. A more title grained approach was needed.</Paragraph> <Paragraph position="6"> In tile second hnplementation, the context machine selected only those propositions which could lead to a goal. Any implication in the knowledge base with the goal as a consequetlt is extracted, as are all assertions that contribute to establishing the troth of any of its antecedents (recursively). The proof is established against this context as a whole. Whilst significantly reducing the size of the msuiting context as well as focussing its content on what the proof might turn out to be, them are problems with this approach. Imagine the situation where Anne has the skill to drive, she owns a car, but she does not have a iicencc because she has to pay her fines.</Paragraph> <Paragraph position="7"> She did not pay her fines because she has no money. All this information would be extracted as a total context for answering the question Cat: At#ne drive? The proof to \[13\] mimicks that of exmnple 2 above, but now, an attempt to establish whether Anne has a licence requires a sub-proof. The proof fails to close on the assumption that Anne has money. It cannot be inferred non-monotonically that Anne has money (because of \[4\]). The answer in this case is No. be, cause Anna has ,no money. Some explanation is due here.</Paragraph> <Paragraph position="8"> Though tile answer offered in the last example is &quot;correct&quot;, and them might he situations in which it is helpful, it is intuitively arguable that an answer No, because Anne ha~ no licence is more helpful. The point is that this version of the context ms, chine does not cater for the possibility of giving this latter answer under any conditions. From this we conclude that a closet interaction between context machine and proof structure is necessary. A helpful answer should not be confined to the ultimate reasons why the reply is No: die answer should depend upon some measure of &quot;closeness&quot; in contexts. Contrary to the assumptions we made at the start of this project our conclusions lead us to postulate that such a view is indeed necessary to pro.</Paragraph> <Paragraph position="9"> vide a fine grained notion of helpfulness.</Paragraph> <Paragraph position="10"> We have no treatment of mutual beliefs so far (but Davies \[19901 is compatible and promising). We need to extend the logic so it can reason with varying domains if we are to exploit full tile intensionality provided by the Property Theory. We have started work on a treatment of time and tense in this framework.</Paragraph> </Section> <Section position="8" start_page="0" end_page="0" type="metho"> <SectionTitle> 7.0 CONCLUSIONS </SectionTitle> <Paragraph position="0"> We have developed a semantic theory of questions using Prop, erty Theory. We have investigated (i) pragmatic answerhood and (it) modality using an experimental computational framework.</Paragraph> <Paragraph position="1"> We believe that the insights gained from the work have bee 0 valuable: they cohtribute towards our understanding of the requkements for a fonnally specified and computationally tractable theory of pragmatics which is capable of incorporating iusights from cognitively oriented theories. Furthermore, the experiment has pointed out that some of the intuitions underlying Relevance Theory are accurate and useful, especially with respect to context refining strategies necessary for characterising helpful answers.</Paragraph> </Section> class="xml-element"></Paper>