## Final Report Summary - MEANCATS (Category theory for meaning assembly and the semantics-pragmatics interface)

MeanCats - Final report

The main goal of the project was the study of the use of a mathematical theory called “Category Theory” to create deep representations of complex meanings in natural language. While linguistic research has produced a satisfying model of how meaning is conveyed by language at a more shallow level, the analysis and representation of more subtle aspect of linguistic meaning is still a young and active area of research. The ability to model these finer aspects of meaning is not only an important scientific endeavour to create a better understanding of language but it is becoming an important are of research that has a direct impact on our society. In fact, as we begin to interact more and more with intelligent machines in our everyday life and our interactions become more complex, it is fundamental for these new technologies to able to have complex exchanges with their users on a par with human-human interactions, and such a level of sophistication requires the ability to understand language in a human like fashion.

The aim of the project was the creation of a mathematical model of how complex meanings are conveyed by language, a model inspired by previous work in the analysis of programming languages. Despite the fact that programming languages are human artefacts, the formalisation of certain aspects of how they translate into certain computations is still an active area of research, and in the last two decades “Category Theory” has an attracted a lot of attention in the programming language semantics community as a mean to capture these finer details of connection between programs and computations. We have used the insight developed in this context and applied them to the case of natural language. In particular we have focused on three linguistic phenomena:

1. the so called “conventional implicatures”, expressions that are used to introduce information in a sort of indirect way, e.g. if a speaker says something along the lines of “John Lee Hooker, the bluesman from Tennessee, appeared in The Blues Brothers” it is not possible for an interlocutor to challenge directly the wrong information that Hooker was born in Tennessee with a simple “No that’s not true” as that would be interpreted to target the information that he was in the Blues Brothers movie;

2. the case of linguistic expressions that seem to interpreted from different point of views, as in the case of a sentence like “Mary Jane loves Peter Parker, but she doesn’t love Spiderman” which does not sound contradictory despite the fact that in the Spiderman universe “Peter Parker” and “Spiderman” refer to the same person;

3. and the case of the expression of uncertainty in language, in particular with respect to how uncertainty is elaborated when multiple uncertain events are expressed.

The first result of the project was the creation of generalised mathematical model of complex meanings are generated in language based on Category Theory and applicable to the phenomena of interests here. The model includes a general way of constructing these meanings and a logical calculus that describes how these meanings emerge from the atomic elements of language (words, morphemes) up to more complex expressions (phrases, sentences and entire discourses). While the phenomena under investigation in this project had already been analysed in the existing literature, their treatment had always suffered from rather “ad hoc” solutions. The model developed during the project offers instead a generalised treatment that can be possibly applied to a wide range of phenomena. Moreover the rigorous formalisation that we have developed has allowed us to clearly state specific assumptions about how these particular types of meaning are used and can be analyses that would have otherwise been hidden in the details of the more “ad hoc” solutions. Our model is not only more general but also more modular, so that the level of analysis can be calibrated on the basis of different needs by adding or removing expressivity to the semantic representations.

The mathematical nature of our analysis meant that we could implement the model and the calculus as an automated theorem prover. The prover automatically generates the complex meaning representations that we are working with, starting from a set of atomic linguistic resources. This is the first step in the application of our work in the context natural language processing technologies, but it is also an important tool for the natural language semantic community. The checking of formal semantic analyses can become a rather daunting task if performed with pen and paper, the prover is a tool that makes this checking easier and less error prone.

The model has also been integrated into two prominent grammatical frameworks, Lexical Functional Grammar (LFG) and Categorial Grammar (CG). Frameworks like LFG and CG are important as they provide the entire toolchain that goes from a “raw” linguistic expression to a representation of its meaning. The fact that our model can be successfully integrated into these kind of frameworks means that it can be indeed used in an applied setting.

Contact details:

Gianluca Giorgolo, gianluca.giorgolo@gmail.com

Ash Asudeh, ash.asudeh@ling-phil.ox.ac.uk

The main goal of the project was the study of the use of a mathematical theory called “Category Theory” to create deep representations of complex meanings in natural language. While linguistic research has produced a satisfying model of how meaning is conveyed by language at a more shallow level, the analysis and representation of more subtle aspect of linguistic meaning is still a young and active area of research. The ability to model these finer aspects of meaning is not only an important scientific endeavour to create a better understanding of language but it is becoming an important are of research that has a direct impact on our society. In fact, as we begin to interact more and more with intelligent machines in our everyday life and our interactions become more complex, it is fundamental for these new technologies to able to have complex exchanges with their users on a par with human-human interactions, and such a level of sophistication requires the ability to understand language in a human like fashion.

The aim of the project was the creation of a mathematical model of how complex meanings are conveyed by language, a model inspired by previous work in the analysis of programming languages. Despite the fact that programming languages are human artefacts, the formalisation of certain aspects of how they translate into certain computations is still an active area of research, and in the last two decades “Category Theory” has an attracted a lot of attention in the programming language semantics community as a mean to capture these finer details of connection between programs and computations. We have used the insight developed in this context and applied them to the case of natural language. In particular we have focused on three linguistic phenomena:

1. the so called “conventional implicatures”, expressions that are used to introduce information in a sort of indirect way, e.g. if a speaker says something along the lines of “John Lee Hooker, the bluesman from Tennessee, appeared in The Blues Brothers” it is not possible for an interlocutor to challenge directly the wrong information that Hooker was born in Tennessee with a simple “No that’s not true” as that would be interpreted to target the information that he was in the Blues Brothers movie;

2. the case of linguistic expressions that seem to interpreted from different point of views, as in the case of a sentence like “Mary Jane loves Peter Parker, but she doesn’t love Spiderman” which does not sound contradictory despite the fact that in the Spiderman universe “Peter Parker” and “Spiderman” refer to the same person;

3. and the case of the expression of uncertainty in language, in particular with respect to how uncertainty is elaborated when multiple uncertain events are expressed.

The first result of the project was the creation of generalised mathematical model of complex meanings are generated in language based on Category Theory and applicable to the phenomena of interests here. The model includes a general way of constructing these meanings and a logical calculus that describes how these meanings emerge from the atomic elements of language (words, morphemes) up to more complex expressions (phrases, sentences and entire discourses). While the phenomena under investigation in this project had already been analysed in the existing literature, their treatment had always suffered from rather “ad hoc” solutions. The model developed during the project offers instead a generalised treatment that can be possibly applied to a wide range of phenomena. Moreover the rigorous formalisation that we have developed has allowed us to clearly state specific assumptions about how these particular types of meaning are used and can be analyses that would have otherwise been hidden in the details of the more “ad hoc” solutions. Our model is not only more general but also more modular, so that the level of analysis can be calibrated on the basis of different needs by adding or removing expressivity to the semantic representations.

The mathematical nature of our analysis meant that we could implement the model and the calculus as an automated theorem prover. The prover automatically generates the complex meaning representations that we are working with, starting from a set of atomic linguistic resources. This is the first step in the application of our work in the context natural language processing technologies, but it is also an important tool for the natural language semantic community. The checking of formal semantic analyses can become a rather daunting task if performed with pen and paper, the prover is a tool that makes this checking easier and less error prone.

The model has also been integrated into two prominent grammatical frameworks, Lexical Functional Grammar (LFG) and Categorial Grammar (CG). Frameworks like LFG and CG are important as they provide the entire toolchain that goes from a “raw” linguistic expression to a representation of its meaning. The fact that our model can be successfully integrated into these kind of frameworks means that it can be indeed used in an applied setting.

Contact details:

Gianluca Giorgolo, gianluca.giorgolo@gmail.com

Ash Asudeh, ash.asudeh@ling-phil.ox.ac.uk