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Bayesian networks are a canonical formalism for representing probabilistic dependencies, yet their integration within logic programming frameworks remains a nontrivial challenge, mainly due to the complex structure of these networks. In…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…
Linear conjunctive grammars are a family of formal grammars with an explicit conjunction operation allowed in the rules, which is notable for its computational equivalence fo one-way real-time cellular automata, also known as trellis…
Determining semantic textual similarity is a core research subject in natural language processing. Since vector-based models for sentence representation often use shallow information, capturing accurate semantics is difficult. By contrast,…
The concept of linearity plays a central role in both mathematics and computer science, with distinct yet complementary meanings. In mathematics, linearity underpins functions and vector spaces, forming the foundation of linear algebra and…
Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms…
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…
A syntax-directed formal system for the development of totally correct programs with respect to an unfair shared-state parallel while-language is proposed. The system can be understood as a compositional reformulation of the Owicki/Gries…
We present a framework for deriving inference relations between Dutch sentence pairs. The proposed framework relies on logic-based reasoning to produce inspectable proofs leading up to inference labels; its judgements are therefore…
We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as…
This paper generalizes the encoding of argumentation frameworks beyond the classical 2-valued propositional logic system ($PL_2$) to 3-valued propositional logic systems ($PL_3$s) and fuzzy propositional logic systems ($PL_{[0,1]}s$),…
We propose a rich foundational theory of typed data streams and stream transformers, motivated by two high-level goals: (1) The type of a stream should be able to express complex sequential patterns of events over time. And (2) it should…
We add to intuitionistic logic infinitely many classical disjunctive tautologies and use the Curry--Howard correspondence to obtain typed concurrent $\lambda$-calculi; each of them features a specific communication mechanism, including…
A line of work in planning uses LLM not to generate a plan, but to generate a formal representation in some planning language, which can be input into a symbolic solver to deterministically find a plan. While showing improved trust and…
The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a…
Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
Despite a growing body of work at the intersection of deep learning and formal languages, there has been relatively little systematic exploration of transformer models for reasoning about typed lambda calculi. This is an interesting area of…