van Benthem, J.

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UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)UvA-DARE (Digital Academic Repository)Dynamic Logic in Natural Languagevan Benthem, J.Publication date2012Document VersionFinal published versionPublished inTheories of everything: in honor of Ed KeenanLink to publicationCitation for published version (APA):van Benthem, J. (2012). Dynamic Logic in Natural Language. In T. Graf, D. Paperno, A.Szabolcsi, & J. Tellings (Eds.), Theories of everything: in honor of Ed Keenan (pp. 18-21).(UCLA Working Papers in Linguistics; No. 17). 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Youwill be contacted as soon as possible.Download date:09 Mar 2023Dynamic Logic in Natural LanguageJohan van Benthem1 When the world was youngAround 1980, a small band of logicians and linguists started collaborating in hopes of getting at the essences underlying natural language semantics by mathematical means. My high  esteem for  Ed  Keenan’s  seminal  work,  and  my long  association  with  him personally, go back to that period, even though I have strayed from the path of natural language since. This is a good occasion to look back – and also ahead. I will give a biased bird’s eye’s view of the history as I see it, then say something about where I have traveled in the meantime, then discuss the possibilities for a safe return.2 Abstract mathematics meets concrete languageMontague  gave  us  the  first  comprehensive  logical  framework  for  thinking  about natural language semantics,  but it  was mainly a highly abstract  machinery for puzzle fitting.  What came afterwards,  in the work of  Ed Keenan (and other  pioneers  whose names  are  all  part  of  a  public  record  that  I  need  not  repeat  here),  was  the  detailed investigation of concrete categories of linguistic expressions – most notably, quantifiers.  Also, moving beyond semantic laws for specific categories, many insights came to light about general linguistic phenomena such as logicality, monotonicity, or iteration, that still  capture audiences today, as I find every time that I lecture about these topics. I vividly remember the excitement at the time in bringing together mathematical structure and the facts of natural language: the eternal hope of science for finding a harmony between pure beauty and understanding the empirical structure of the world. Ed sought that harmony mainly using methods from algebra,  I myself  preferred model  theory – but  those are details, the spirit is the same.3 From description to functionThe main emphasis in this approach to semantics was on the expressive power of natural languages, that is the extent to which they describe the world. This focus singled out  certain  kinds  of  expression  for  special  attention:  logical  constants  as  describing complex facts, generalized quantifiers as structuring what we say about objects, and, say, temporal  expressions expressing how things proceed through time.  But  in  the  1980s, semantics also developed innovations that shift this perspective. Discourse representation theory is already more about what you do with language, rather than its expressive power,  and this theme of  functions of language use is even clearer in paradigms like dynamic semantics or game theoretical semantics. In this more functional perspective, the issue becomes understanding, not how much natural language can say about the world, but  © 2012 This is an open-access article distributed under the terms of a Creative Commons Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/).Johan van BenthemUCLA Working Papers in Linguistics, Theories of Everything Volume 17, Article 4: 18-21, 2012how good it is at facilitating the major purposes that it serves for us: communication and general coordination of behavior. If you wish, the aim becomes ‘functional completeness’ for procedures used by humans rather than ‘expressive completeness’ with respect to the world. This richer view is still developing today, and interestingly, it also has counterparts in  computational  formalisms  – the third  partner  in  Montague’s  Circle  of  natural  and formal languages. Computational languages and models today are connected by a web of  automata  and  games  of  verification  and  comparison,  whose  theory  is  transforming traditional  subjects  like  formal  language  theory or  model  theory.  My own ‘semantic automata’ for quantifiers  around 1985 were already a step in  this direction,  and it  is  perhaps no coincidence that they have been reviving recently.4 Enter new disciplinesModeling functions of language may be a less focused enterprise than earlier work in formal semantics, since mining a function of natural language, or a form of its dynamic use, is harder than mining, say, a syntactic lexicon. On the other hand, what helps is that  we now enter a territory where other disciplines are active, not just linguistics. Functions such as information transfer, learning, or more general forms of communication exhibit natural process structure that can be, and has been, studied on its own, in epistemology, in computational studies of agent systems, or in game theory.5 Enter new logicsProcess structure involves information states, transitions, and agents.  This quickly leads us to other streams in logic than the type theories or intensional logics traditionally employed in formal semantics, including various systems of dynamic logic (and others might well be relevant). In particular, in recent years, I have been involved with dynamic epistemic  logics of  information-driven  interactive  agency and the  resulting  interfaces between logic, computer science, and game theory. These systems move many new topics into the scope of explicit logical analysis, such as the effects of events of getting hard or  soft information, acts of inference, questions and answers, but also events that change preferences, or the working of strategies, all important features of rational agency.6 A natural dualityI find the two perspectives on language outlined here very natural companions. They also  represent  the  two  main  historical  functions  of  logic:  as  a  medium  for  world description, but also as an account of argumentative procedure. For instance, when you take your first course in logic, you will see these dual aspects reflected in the two ways you can think of propositional logic: as a theory of complex facts and classifications, or as a theory of discourse control describing how you refute or outwit opponents. The same two faces return in our best accounts of the very logical constants. Sometimes, they are ways of structuring invariants (in the line of the permutation invariance for linguistic expressions  that  Ed and  I  have  mainly concentrated  on  over  the  years),  but  equally fundamentally, they are expression of functional control, as one can see in game-theoretic views of the Boolean operations as choices or role switchers. Again, this duality is far Dynamic Logic in Natural Language 19from completely understood or explored, and personally, I am now inclined to think of even punctuation markers like ? , ! like bona fide function-oriented logical operations.7 The dynamic repertoire of natural language But natural language has not gone away in all this. While it is true that most work in agent systems or game theory (or related areas of philosophy such as social epistemology or ethics) does not pay systematic attention to how things would be said in linguistic  form, there remains the undeniable fact that much of what rational (and not so rational) agents do is soaked in natural language, being either triggered by or at least facilitated by  what people say. I am getting more and more interested in getting clearer on this, though it does seem to involve a shift in the focus of attention. 8 Which lexical items?Traditionally,  we have chosen a few expressions to lavish our attention on. These were  the  logical  constants,  perhaps  because  of  their  mathematical  pedigree,  the quantifiers perhaps for similar reasons, and the occasional odd verb for its philosophical  credentials, such as “know”. But if our core interests come to include information and communication, why would this be the only, or even the most obvious choice of lexical  items to focus on right at the start? In a functional perspective, we want to understand the semantics  of  expressions  reflecting  the  rich  human  repertoire  of  cognitive  attitudes: knowing,  believing,  supposing,  doubting,  seeing,  etc.  Of  course,  some  authors  in philosophical logic have done quite a bit of this – I am not claiming that we have to start  from scratch. I also observe that the current semantic literature has sophisticated accounts of epistemic modals “may” and “must”, partly triggered by concerns in philosophy, and these are now opening the way to the study of a much wider range of plausibilistic and probabilistic expressions going beyond the traditional agenda of formal semantics. Still, to mention one more potential case of bias beyond lexical selection, traditional semantics  has focused on ‘hard information’ that is totally reliable, but this is only a tiny fraction of actual language use. A much better paradigm for understanding how language functions might be ‘soft attitudes’ like belief, based on plausibility rather than on truth. If belief revision and learning are of the essence in human behavior, their ‘correction dynamics’  might be expected to be at the heart of the functioning of natural language, too.9 Action features at center stage Returning to function and cognitive action again, even sticking to knowledge, from a dynamic perspective, this is just a temporary attitude that gets transformed continually by new dynamic actions. Thus, “know” becomes a member of a close family of verbs like “concluding”, “learning”, and perhaps even “giving up” and “forgetting”. Likewise, still in this same family of function words, we would expect the core to include actions like assert, reject, agree, observe, see, correct, … Speech act theories have addressed several  of these, but they went only so far. What the experience in dynamic-epistemic logic of the last decade has shown is that these expressions are just as logical as traditional ones in  admitting  complete  logics  with  a  perspicuous  model  theory.  And  they may be  more 20 van Benthemimportant  to  understanding  natural  language  than  rarified  intricacies  of  ambiguity or branching in  quantification,  that  never seem to prevent  anyone from learning foreign languages, or from communicating successfully across linguistic barriers. 10  A return to semantics of natural language?One of my many promises to myself (and maybe now also to Ed) has been a return to logical  semantics  of  natural  language in this  double  sense of  logical:  descriptive and functional.  But  this may involve more than doing semantics of more lexical items or further syntactic constructions, whether static or dynamic in the preceding senses. The functional picture of language involves modeling the basic types of agent and the nature of the processes that they are involved in. There is no need to suppose that all crucial  aspects of this are encoded in syntax, or that what is encoded in syntax is the same across  human languages. This broader desideratum has already been noted in the literature on Amsterdam-style  dynamic  semantics  for  natural  language,  where  the  nature  of  the linguistic agents and the precise processes underpinning the idea of information change have remained mostly implicit so far. Here dynamic-epistemic logics take a more explicit  approach modeling communicative actions of any sort, harder or softer, more private or more public, whether or not corresponding precisely to linguistic utterances – though, Heaven knows, more structure may have to be added. Yes, I know that some people call  this further enterprise pragmatics, and hence something that can be safely set aside as work for others. But if modern logic can deal with both, why separate what seems a natural unity in the way we use natural language?Whether the above represents a return to natural language in the sense of the 1980s may be a moot point then, though I do think of that exciting period as opening horizons,  and not as fixing some orthodox view of what can legitimately be studied. Moreover, one of the things that has always set Ed’s work apart in the field (and made it so original) has been its abstraction level, and its search for semantic universals of expressive power that transcended the details of the formal systems of the day. I would think that the above thoughts, viewed as a search for logical universals of functional power, are in the same  spirit – whether concrete natural language syntax is our main guide or other, less obvious, and perhaps more subtle, invariants of linguistic practice.AffiliationJohan van BenthemUniversity of Amsterdamjohan@science.uva.nlStanford Universityjohan@csli.stanford.eduDynamic Logic in Natural Language 21

Dynamic Logic in Natural Language

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Dynamic Logic in Natural Language

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