Lawrence Moss | Indiana University (original) (raw)
Papers by Lawrence Moss
Computational Linguistics
Against the backdrop of the ever-improving Natural Language Inference (NLI) models, recent effort... more Against the backdrop of the ever-improving Natural Language Inference (NLI) models, recent efforts have focused on the suitability of the current NLI datasets and on the feasibility of the NLI task as it is currently approached. Many of the recent works have exposed the inherent human disagreements of the inference task and have proposed a shift from categorical labels to human subjective probability assessments, capturing human uncertainty. In this work, we show how neither the current task formulation nor the proposed uncertainty gradient are entirely suitable for solving the NLI challenges. Instead, we propose an ordered sense space annotation, which distinguishes between logical and common-sense inference. One end of the space captures non-sensical inferences, while the other end represents strictly logical scenarios. In the middle of the space, we find a continuum of commonsense, i.e., the subjective and graded opinion of a “person on the street”. To arrive at the proposed anno...
ArXiv, 2022
We consider dynamic versions of epistemic logic as formulated in [1]. That paper proposed a famil... more We consider dynamic versions of epistemic logic as formulated in [1]. That paper proposed a family of logical languages L(Σ) parameterized by action signatures. In addition to L(Σ), we consider two fragments L0(Σ) and L1(Σ) of it. We review the syntax and semantics of these languages L0(Σ),L1(Σ), and L(Σ), as well as the sound proof systems for the validities in them. It was shown in [13] that validity in L(Σ) is Π 1 -complete, so there are no recursively axiomatized complete logical systems for it. On the positive side, this paper proves the strong completeness of the axiomatization of L0(Σ) and the weak completeness of L1(Σ). The work involve a detour into term rewriting theory. And since at the heart of the argument is modal filtration, it gives the finite model property and hence decidability. We also give a translation of L1(Σ) into PDL, hence we obtain a second proof of the decidability of L1(Σ). The paper closes with some results on expressive power. These are mostly concerne...
Probabilistic rules “if A then B” rules are typically formalized as Bayesian conditionals P (B|A)... more Probabilistic rules “if A then B” rules are typically formalized as Bayesian conditionals P (B|A), as many (e.g., Pearl) have argued that Bayesian conditionals are the correct way to think about such rules. However, there are challenges with standard inferences such as modus ponens, modus tollens, and rule chaining that might make probabilistic material implication a better candidate at times for rule-based systems employing forward-chaining; and arguably material implication is still suitable when information about prior or conditional probabilities is not available. We compare a probabilistic version of the material conditional from classical logic with Bayesian conditionals in the setting of interval-valued probability theory. We give quantitative treatments of familiar rules from logic to arrive at the best possible bounds on inferences in rule-based systems constituting directed acyclic graphs. Introduction. The discussion of how to best render formally the intuitions behind “i...
There are several issues which every theory of information and information-flow must address. Amo... more There are several issues which every theory of information and information-flow must address. Among these are the role of perspective and background on inference. There is an intuition that information is relative to the observer or recipient; but a thoroughgoing relativism on this point seems to contradict another intuition, that information is an inherent property of parts of the world and facts which they might support. A second issue is to clarify what it means to say that sources of information are usually reliable but sometimes fallible. ...
Acknowledgements First and foremost, I am indebted to Yoad Winter. Yoad is everything one would e... more Acknowledgements First and foremost, I am indebted to Yoad Winter. Yoad is everything one would expect to find in an advisor and a teacher, and much more than this. Yoad is the one who introduced me to the field of natural language semantics. His optimism and encouragement, together with the endless discussions and iterations we had, made the completion of this thesis possible. Special thanks to Nissim Francez for the time and effort he put into Chapter 3, which is based on a conference paper we published together, and for his thorough remarks on the material in the other chapters. Nissim, as a teacher, has initiated my interest in Categorial Grammars and Proof Theory. Thanks also to the other members in my PhD committee, Johann Makowsky and Ariel Cohen, for their illuminating remarks. I am grateful to Shalom Lappin, Ed Keenan, Johann Makowsky, and especially to Ya’acov Peterzil, for their remarks on the material in Chapter 4.
Proceedings of the Seventh Joint Conference on Lexical and Computational Semantics, 2018
We discuss what is known about logical reasoning concerning the sizes of sets, including expressi... more We discuss what is known about logical reasoning concerning the sizes of sets, including expressions like there are at least as many x as y, there are more x than y, and most x are y. It turns out that reasoning with expressions like this can be done efficiently, that formal proofs can be obtained which do not employ translation to standard logic, and that counter-models can also be generated. The paper also contains a new result, a completeness theorem for syllogistic reasoning involving the sentences in our fragment, and adding sentential negation. So we are not done with the project of getting a complete logics for reasoning about sizes of sets. At the same time, there are some open questions. We show one implementation. We mention briefly some very new work which allows one to do logical reasoning on sentences as they come (not from a toy grammar), but at some cost. Finally, we discuss connections to cognitive science, many of which are waiting to be made.
ArXiv, 2020
We present a new logic-based inference engine for natural language inference (NLI) called MonaLog... more We present a new logic-based inference engine for natural language inference (NLI) called MonaLog, which is based on natural logic and the monotonicity calculus. In contrast to existing logic-based approaches, our system is intentionally designed to be as lightweight as possible, and operates using a small set of well-known (surface-level) monotonicity facts about quantifiers, lexical items and tokenlevel polarity information. Despite its simplicity, we find our approach to be competitive with other logic-based NLI models on the SICK benchmark. We also use MonaLog in combination with the current state-of-the-art model BERT in a variety of settings, including for compositional data augmentation. We show that MonaLog is capable of generating large amounts of high-quality training data for BERT, improving its accuracy on SICK.
We discuss what is known about implementations of logical systems whose syntax is either a small ... more We discuss what is known about implementations of logical systems whose syntax is either a small fragment of natural language, or alternatively is a formal language which looks more like natural language than standard logical systems. Much of this work in this area is now carried out under the name of natural logic. Just as in modal logic or description logic, there are many systems of natural logic; indeed, some of those systems have features reminiscent of modal logic and description logic. For the most part, quantification in natural logics looks more like description logic or term logic (i.e., syllogistic logic) than first-order logic. The main design criteria for natural logics are that (1) one can be able to use them to carry out significant parts of reasoning; and (2) they should be decidable, and indeed algorithmically manageable. All of the questions that we ask about the implementation of any logics can be asked about natural logics. This paper surveys what is known in the...
This paper presents an ongoing research project called “natural logic” and makes the case that it... more This paper presents an ongoing research project called “natural logic” and makes the case that it is relevant to AI, Computational Linguistics, and Cognitive Science. We propose to add some of the natural logic modules which have already been developed to existing NLP systems. We see our approach as complementing and augmenting data-driven approaches exemplified by IBM’s Watson. We give a brief introduction to natural logic and present examples of proofs that can be given in a working system. We furthermore introduce monotonic logic, another promising approach for extracting information from sentences that contain quantifiers. We finish the paper by presenting some early work that integrates syllogistic reasoning into exsiting NLP systems. Introduction The history of logic and AI is a checkered one. Starting with huge optimism, the idea of applying logic in AI and NLP is very much a minority one today. The 2015 report of the One Hundred Year Study on Artificial Intelligence states t...
Supersymmetry is an idea that has played a critical role in many of the recent developments in th... more Supersymmetry is an idea that has played a critical role in many of the recent developments in theoretical physics of interest to mathematicians. The third volume of The quantum theory of fields by Steven Weinberg [1] is an introduction to supersymmetric field theory and supergravity. The first two volumes of the series treat the essentials of quantum field theory. In this third volume, Weinberg has created the most complete introduction to supersymmetry to date. Although the text is aimed squarely at physicists, it should prove useful to mathematicians interested in learning about supersymmetry in its natural physical setting. As a supplement, to help bridge the cultural and language differences between physics and mathematics, I would suggest the short lecture series by Freed [2]. My goal, in the course of this review, is to convey both the essential idea behind supersymmetry and some of the background needed to peruse the physics literature. What is supersymmetry? The basic notio...
The Review of Symbolic Logic, 2020
This paper explores relational syllogistic logics, a family of logical systems related to reasoni... more This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and complexity results for a natural subfamily of relational syllogistic logics, parametrized by constructors for terms and for sentences.
Lecture Notes in Computer Science, 2020
We study the synthesis problem for systems with a parameterized number of processes. As in the cl... more We study the synthesis problem for systems with a parameterized number of processes. As in the classical case due to Church, the system selects actions depending on the program run so far, with the aim of fulfilling a given specification. The difficulty is that, at the same time, the environment executes actions that the system cannot control. In contrast to the case of fixed, finite alphabets, here we consider the case of parameterized alphabets. An alphabet reflects the number of processes, which is static but unknown. The synthesis problem then asks whether there is a finite number of processes for which the system can satisfy the specification. This variant is already undecidable for very limited logics. Therefore, we consider a first-order logic without the order on word positions. We show that even in this restricted case synthesis is undecidable if both the system and the environment have access to all processes. On the other hand, we prove that the problem is decidable if th...
Proceedings of the AAAI Conference on Artificial Intelligence, 2020
This paper presents the most basic logics for reasoning about the sizes of sets that admit either... more This paper presents the most basic logics for reasoning about the sizes of sets that admit either the union of terms or the intersection of terms. That is, our logics handle assertions All x y and AtLeast x y, where x and y are built up from basic terms by either unions or intersections. We present a sound, complete, and polynomial-time decidable proof system for these logics. An immediate consequence of our work is the completeness of the logic additionally permitting More x y. The logics considered here may be viewed as efficient fragments of two logics which appear in the literature: Boolean Algebra with Presburger Arithmetic and the Logic of Comparative Cardinality.
Foundations of Software Science and Computation Structures, 2020
EasyChair Preprints, Jun 2, 2018
Proceedings of the 13th International Conference on Computational Semantics - Short Papers, 2019
The Bulletin of Symbolic Logic, 2016
Computational Linguistics
Against the backdrop of the ever-improving Natural Language Inference (NLI) models, recent effort... more Against the backdrop of the ever-improving Natural Language Inference (NLI) models, recent efforts have focused on the suitability of the current NLI datasets and on the feasibility of the NLI task as it is currently approached. Many of the recent works have exposed the inherent human disagreements of the inference task and have proposed a shift from categorical labels to human subjective probability assessments, capturing human uncertainty. In this work, we show how neither the current task formulation nor the proposed uncertainty gradient are entirely suitable for solving the NLI challenges. Instead, we propose an ordered sense space annotation, which distinguishes between logical and common-sense inference. One end of the space captures non-sensical inferences, while the other end represents strictly logical scenarios. In the middle of the space, we find a continuum of commonsense, i.e., the subjective and graded opinion of a “person on the street”. To arrive at the proposed anno...
ArXiv, 2022
We consider dynamic versions of epistemic logic as formulated in [1]. That paper proposed a famil... more We consider dynamic versions of epistemic logic as formulated in [1]. That paper proposed a family of logical languages L(Σ) parameterized by action signatures. In addition to L(Σ), we consider two fragments L0(Σ) and L1(Σ) of it. We review the syntax and semantics of these languages L0(Σ),L1(Σ), and L(Σ), as well as the sound proof systems for the validities in them. It was shown in [13] that validity in L(Σ) is Π 1 -complete, so there are no recursively axiomatized complete logical systems for it. On the positive side, this paper proves the strong completeness of the axiomatization of L0(Σ) and the weak completeness of L1(Σ). The work involve a detour into term rewriting theory. And since at the heart of the argument is modal filtration, it gives the finite model property and hence decidability. We also give a translation of L1(Σ) into PDL, hence we obtain a second proof of the decidability of L1(Σ). The paper closes with some results on expressive power. These are mostly concerne...
Probabilistic rules “if A then B” rules are typically formalized as Bayesian conditionals P (B|A)... more Probabilistic rules “if A then B” rules are typically formalized as Bayesian conditionals P (B|A), as many (e.g., Pearl) have argued that Bayesian conditionals are the correct way to think about such rules. However, there are challenges with standard inferences such as modus ponens, modus tollens, and rule chaining that might make probabilistic material implication a better candidate at times for rule-based systems employing forward-chaining; and arguably material implication is still suitable when information about prior or conditional probabilities is not available. We compare a probabilistic version of the material conditional from classical logic with Bayesian conditionals in the setting of interval-valued probability theory. We give quantitative treatments of familiar rules from logic to arrive at the best possible bounds on inferences in rule-based systems constituting directed acyclic graphs. Introduction. The discussion of how to best render formally the intuitions behind “i...
There are several issues which every theory of information and information-flow must address. Amo... more There are several issues which every theory of information and information-flow must address. Among these are the role of perspective and background on inference. There is an intuition that information is relative to the observer or recipient; but a thoroughgoing relativism on this point seems to contradict another intuition, that information is an inherent property of parts of the world and facts which they might support. A second issue is to clarify what it means to say that sources of information are usually reliable but sometimes fallible. ...
Acknowledgements First and foremost, I am indebted to Yoad Winter. Yoad is everything one would e... more Acknowledgements First and foremost, I am indebted to Yoad Winter. Yoad is everything one would expect to find in an advisor and a teacher, and much more than this. Yoad is the one who introduced me to the field of natural language semantics. His optimism and encouragement, together with the endless discussions and iterations we had, made the completion of this thesis possible. Special thanks to Nissim Francez for the time and effort he put into Chapter 3, which is based on a conference paper we published together, and for his thorough remarks on the material in the other chapters. Nissim, as a teacher, has initiated my interest in Categorial Grammars and Proof Theory. Thanks also to the other members in my PhD committee, Johann Makowsky and Ariel Cohen, for their illuminating remarks. I am grateful to Shalom Lappin, Ed Keenan, Johann Makowsky, and especially to Ya’acov Peterzil, for their remarks on the material in Chapter 4.
Proceedings of the Seventh Joint Conference on Lexical and Computational Semantics, 2018
We discuss what is known about logical reasoning concerning the sizes of sets, including expressi... more We discuss what is known about logical reasoning concerning the sizes of sets, including expressions like there are at least as many x as y, there are more x than y, and most x are y. It turns out that reasoning with expressions like this can be done efficiently, that formal proofs can be obtained which do not employ translation to standard logic, and that counter-models can also be generated. The paper also contains a new result, a completeness theorem for syllogistic reasoning involving the sentences in our fragment, and adding sentential negation. So we are not done with the project of getting a complete logics for reasoning about sizes of sets. At the same time, there are some open questions. We show one implementation. We mention briefly some very new work which allows one to do logical reasoning on sentences as they come (not from a toy grammar), but at some cost. Finally, we discuss connections to cognitive science, many of which are waiting to be made.
ArXiv, 2020
We present a new logic-based inference engine for natural language inference (NLI) called MonaLog... more We present a new logic-based inference engine for natural language inference (NLI) called MonaLog, which is based on natural logic and the monotonicity calculus. In contrast to existing logic-based approaches, our system is intentionally designed to be as lightweight as possible, and operates using a small set of well-known (surface-level) monotonicity facts about quantifiers, lexical items and tokenlevel polarity information. Despite its simplicity, we find our approach to be competitive with other logic-based NLI models on the SICK benchmark. We also use MonaLog in combination with the current state-of-the-art model BERT in a variety of settings, including for compositional data augmentation. We show that MonaLog is capable of generating large amounts of high-quality training data for BERT, improving its accuracy on SICK.
We discuss what is known about implementations of logical systems whose syntax is either a small ... more We discuss what is known about implementations of logical systems whose syntax is either a small fragment of natural language, or alternatively is a formal language which looks more like natural language than standard logical systems. Much of this work in this area is now carried out under the name of natural logic. Just as in modal logic or description logic, there are many systems of natural logic; indeed, some of those systems have features reminiscent of modal logic and description logic. For the most part, quantification in natural logics looks more like description logic or term logic (i.e., syllogistic logic) than first-order logic. The main design criteria for natural logics are that (1) one can be able to use them to carry out significant parts of reasoning; and (2) they should be decidable, and indeed algorithmically manageable. All of the questions that we ask about the implementation of any logics can be asked about natural logics. This paper surveys what is known in the...
This paper presents an ongoing research project called “natural logic” and makes the case that it... more This paper presents an ongoing research project called “natural logic” and makes the case that it is relevant to AI, Computational Linguistics, and Cognitive Science. We propose to add some of the natural logic modules which have already been developed to existing NLP systems. We see our approach as complementing and augmenting data-driven approaches exemplified by IBM’s Watson. We give a brief introduction to natural logic and present examples of proofs that can be given in a working system. We furthermore introduce monotonic logic, another promising approach for extracting information from sentences that contain quantifiers. We finish the paper by presenting some early work that integrates syllogistic reasoning into exsiting NLP systems. Introduction The history of logic and AI is a checkered one. Starting with huge optimism, the idea of applying logic in AI and NLP is very much a minority one today. The 2015 report of the One Hundred Year Study on Artificial Intelligence states t...
Supersymmetry is an idea that has played a critical role in many of the recent developments in th... more Supersymmetry is an idea that has played a critical role in many of the recent developments in theoretical physics of interest to mathematicians. The third volume of The quantum theory of fields by Steven Weinberg [1] is an introduction to supersymmetric field theory and supergravity. The first two volumes of the series treat the essentials of quantum field theory. In this third volume, Weinberg has created the most complete introduction to supersymmetry to date. Although the text is aimed squarely at physicists, it should prove useful to mathematicians interested in learning about supersymmetry in its natural physical setting. As a supplement, to help bridge the cultural and language differences between physics and mathematics, I would suggest the short lecture series by Freed [2]. My goal, in the course of this review, is to convey both the essential idea behind supersymmetry and some of the background needed to peruse the physics literature. What is supersymmetry? The basic notio...
The Review of Symbolic Logic, 2020
This paper explores relational syllogistic logics, a family of logical systems related to reasoni... more This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and complexity results for a natural subfamily of relational syllogistic logics, parametrized by constructors for terms and for sentences.
Lecture Notes in Computer Science, 2020
We study the synthesis problem for systems with a parameterized number of processes. As in the cl... more We study the synthesis problem for systems with a parameterized number of processes. As in the classical case due to Church, the system selects actions depending on the program run so far, with the aim of fulfilling a given specification. The difficulty is that, at the same time, the environment executes actions that the system cannot control. In contrast to the case of fixed, finite alphabets, here we consider the case of parameterized alphabets. An alphabet reflects the number of processes, which is static but unknown. The synthesis problem then asks whether there is a finite number of processes for which the system can satisfy the specification. This variant is already undecidable for very limited logics. Therefore, we consider a first-order logic without the order on word positions. We show that even in this restricted case synthesis is undecidable if both the system and the environment have access to all processes. On the other hand, we prove that the problem is decidable if th...
Proceedings of the AAAI Conference on Artificial Intelligence, 2020
This paper presents the most basic logics for reasoning about the sizes of sets that admit either... more This paper presents the most basic logics for reasoning about the sizes of sets that admit either the union of terms or the intersection of terms. That is, our logics handle assertions All x y and AtLeast x y, where x and y are built up from basic terms by either unions or intersections. We present a sound, complete, and polynomial-time decidable proof system for these logics. An immediate consequence of our work is the completeness of the logic additionally permitting More x y. The logics considered here may be viewed as efficient fragments of two logics which appear in the literature: Boolean Algebra with Presburger Arithmetic and the Logic of Comparative Cardinality.
Foundations of Software Science and Computation Structures, 2020
EasyChair Preprints, Jun 2, 2018
Proceedings of the 13th International Conference on Computational Semantics - Short Papers, 2019
The Bulletin of Symbolic Logic, 2016