Related papers: Formalizing Representation Theorems for a Logical …
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
Many automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter when translating monomorphic to…
Historical approaches to Table Representation Learning (TRL) have largely adopted the sequential paradigms of Natural Language Processing (NLP). We argue that this linearization of tables discards their essential geometric and relational…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Lambda-calculi come with no fixed evaluation strategy. Different strategies may then be considered, and it is important that they satisfy some abstract rewriting property, such as factorization or normalization theorems. In this paper we…
This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics. Cumulative logics are famously given by System C. For propositional…
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…
Machine learning models increasingly function as representational systems, yet the philosoph- ical assumptions underlying their internal structures remain largely unexamined. This paper develops a structuralist decision framework for…
Advances in natural language processing have resulted in increased capabilities with respect to multiple tasks. One of the possible causes of the observed performance gains is the introduction of increasingly sophisticated text…
In recent years, transformer-based language representation models (LRMs) have achieved state-of-the-art results on difficult natural language understanding problems, such as question answering and text summarization. As these models are…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
Reynold's parametricity theory captures the property that parametrically polymorphic functions behave uniformly: they produce related results on related instantiations. In dependently-typed programming languages, such relations and…
Recent work exhibited that distributed word representations are good at capturing linguistic regularities in language. This allows vector-oriented reasoning based on simple linear algebra between words. Since many different methods have…
Propositional and modal inclusion logic are formalisms that belong to the family of logics based on team semantics. This article investigates the model checking and validity problems of these logics. We identify complexity bounds for both…
We address a general representation problem for belief change, and describe two interrelated representations for iterative non-prioritized change: a logical representation in terms of persistent epistemic states, and a constructive…
This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of `maximal formula', `segment' and `maximal segment' suitable to the system, and gives…
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…
We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is…