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The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is…
The Dependent Object Types (DOT) calculus formalizes key features of Scala. The D$_{<: }$ calculus is the core of DOT. To date, presentations of D$_{<: }$ have used declarative typing and subtyping rules, as opposed to algorithmic.…
The $N$th power of a polynomial matrix of fixed size and degree can be computed by binary powering as fast as multiplying two polynomials of linear degree in~$N$. When Fast Fourier Transform (FFT) is available, the resulting complexity is…
Semantic data fuels many different applications, but is still lacking proper integration into programming languages. Untyped access is error-prone while mapping approaches cannot fully capture the conceptualization of semantic data. In this…
Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
Virtually all verification and synthesis techniques assume that the formal specifications are readily available, functionally correct, and fully match the engineer's understanding of the given system. However, this assumption is often…
Linear Logic was introduced by Girard as a resource-sensitive refinement of classical logic. It turned out that full propositional Linear Logic is undecidable (Lincoln, Mitchell, Scedrov, and Shankar) and, hence, it is more expressive than…
We give an interpretation of full classical linear logic, and linear proofs in terms of operations on the blockchain.
Practically all of the planning research is limited to states represented in terms of Boolean and numeric state variables. Many practical problems, for example, planning inside complex software systems, require far more complex data types,…
A natural liberalization of Datalog is used in the Distributed Knowledge Authorization Language (DKAL). We show that the expressive power of this liberal Datalog is that of existential fixed-point logic. The exposition is self-contained.
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…
We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification…
In this paper we present the new logic programming language DALI, aimed at defining agents and agent systems. A main design objective for DALI has been that of introducing in a declarative fashion all the essential features, while keeping…
Data science workflows often integrate functionalities from a diverse set of libraries and frameworks. Tasks such as debugging require data lineage that crosses library boundaries. The problem is that the way that "lineage" is represented…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
We introduce Reasoning Core, a new scalable environment for Reinforcement Learning with Verifiable Rewards (RLVR), designed to advance foundational symbolic reasoning in Large Language Models (LLMs). Unlike existing benchmarks that focus on…
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…