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Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
Mathematical reasoning is central to artificial intelligence, with applications in education, code generation, and research-level mathematical discovery. Mathematical competitions highlight two problem types: theorem proving, requiring…
We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
We need much better understanding of information processing and computation as its primary form. Future progress of new computational devices capable of dealing with problems of big data, internet of things, semantic web, cognitive robotics…
Neural-symbolic methods have demonstrated efficiency in enhancing the reasoning abilities of large language models (LLMs). However, existing methods mainly rely on syntactically mapping natural languages to complete formal languages like…
Abraham Robinson's philosophical stance has been the subject of several recent studies. Erhardt following Gaifman claims that Robinson was a finitist, and that there is a tension between his philosophical position and his actual…
While recent progress in quantum hardware open the door for significant speedup in certain key areas (cryptography, biology, chemistry, optimization, machine learning, etc), quantum algorithms are still hard to implement right, and the…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
In this chapter, we argue for an epistemological shift from viewing coding and computational thinking as mastery over computational logic and symbolic forms, to viewing them as a more complex form of experience. Rather than viewing…
Automatic (i.e., computer-assisted) theorem proving (ATP) can come in many flavors. This document presents early steps in our effort towards defining object-oriented theorem proving (OOTP) as a new style of ATP. Traditional theorem proving…
Metamodeling is a general approach to expressing knowledge about classes and properties in an ontology. It is a desirable modeling feature in multiple applications that simplifies the extension and reuse of ontologies. Nevertheless,…
Emerging research frontiers and computational advances have gradually transformed cognitive science into a multidisciplinary and data-driven field. As a result, there is a proliferation of cognitive theories investigated and interpreted…
This paper argues that explainability is only one facet of a broader ideal that shapes our expectations towards artificial intelligence (AI). Fundamentally, the issue is to what extent AI exhibits systematicity--not merely in being…
Context: To reduce manual effort of extracting test cases from natural-language requirements, many approaches based on Natural Language Processing (NLP) have been proposed in the literature. Given the large amount of approaches in this…
Recent approaches to verifying programs in separation logics for concurrency have used state transition systems (STSs) to specify the atomic operations of programs. A key challenge in the setting has been to compose such STSs into larger…
This book presents a methodology and philosophy of empirical science based on large scale lossless data compression. In this view a theory is scientific if it can be used to build a data compression program, and it is valuable if it can…
Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been…