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We investigate how language models handle the proviso problem, an unresolved issue in pragmatics where presuppositions in conditional sentences diverge between theoretical and human interpretations. We reformulate this phenomenon as a…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for…
The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation. We consider the problem with the additional feature that agents' preferences involve uncertainty. The setting with…
The study explores the capabilities of OpenAI's ChatGPT in solving different types of physics problems. ChatGPT (with GPT-4) was queried to solve a total of 40 problems from a college-level engineering physics course. These problems ranged…
Computer science students often struggle with abstract theoretical concepts, particularly in introductory courses on theoretical computer science. One such challenge is understanding context-free languages and their various representations.…
The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum…
Large Language Models (LLMs) have become a popular choice for many Natural Language Processing (NLP) tasks due to their versatility and ability to produce high-quality results. Specifically, they are increasingly used for automatic code…
Conversational practice, while crucial for all language learners, can be challenging to get enough of and very expensive. Chatbots are computer programs developed to engage in conversations with humans. They are designed as software avatars…
The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
Mathematical text is written using a combination of words and mathematical expressions. This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
Knowing the truth is rarely enough -- we also seek out reasons why the fact is true. While much is known about how we explain contingent truths, we understand less about how we explain facts, such as those in mathematics, that are true as a…
The relationship between the complexity classes P and NP is a question that has not yet been answered by the Theory of Computation. The existence of a language in NP, proven not to belong to P, is sufficient evidence to establish the…
ChatGPT took the world by storm for its impressive abilities. Due to its release without documentation, scientists immediately attempted to identify its limits, mainly through its performance in natural language processing (NLP) tasks. This…
Deep probabilistic programming languages try to combine the advantages of deep learning with those of probabilistic programming languages. If successful, this would be a big step forward in machine learning and programming languages.…
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
Probabilistic systems are an important theme in AI domain. As the specification language, the logic PCTL is now the default logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic…
Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are…
In machine translation, a common problem is that the translation of certain words even if translated can cause incomprehension of the target language audience due to different cultural backgrounds. A solution to solve this problem is to add…