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Despite the impressive growth of the abilities of multilingual language models, such as XLM-R and mT5, it has been shown that they still face difficulties when tackling typologically-distant languages, particularly in the low-resource…

The interpretation of propositional dynamic logic (PDL) through Kripke models requires the relations constituting the interpreting Kripke model to closely observe the syntax of the modal operators. This poses a significant challenge for an…

Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…

We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…

Larsen and Skou characterized probabilistic bisimilarity over reactive probabilistic systems with a logic including true, negation, conjunction, and a diamond modality decorated with a probabilistic lower bound. Later on, Desharnais,…

We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…

Rewriting logic is naturally concurrent: several subterms of the state term can be rewritten simultaneously. But state terms are global, which makes compositionality difficult to achieve. Compositionality here means being able to decompose…

Logically constrained rewrite systems (LCTRSs) are a versatile and efficient rewriting formalism that can be used to model programs from various programming paradigms, as well as simplification systems in compilers and SMT solvers. In this…

With good explanatory power and controllability, rule-based methods play an important role in many tasks such as knowledge reasoning and decision support. However, existing studies primarily focused on learning chain-like rules, which limit…

We propose a reinforcement-learning algorithm to tackle the challenge of reconstructing phylogenetic trees. The search for the tree that best describes the data is algorithmically challenging, thus all current algorithms for phylogeny…

We present a propositional modal logic $\sf WC$, which includes a logical $verum$ constant $\top$ but does not have any propositional variables. Furthermore, the only connectives in the language of $\sf WC$ are consistency-operators…

This work focuses on the problem of exact model reduction of positive linear systems, by leveraging minimal realization theory. While determining the existence of a positive reachable realization remains in general an open problem, we are…

Tree search methods have demonstrated impressive performance in code generation. Previous methods combine tree search with reflection that summarizes past mistakes to achieve iterative improvement. However, these methods face significant…

Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…

This paper presents the logic QRC$_1$, which is a strictly positive fragment of quantified modal logic. The intended reading of the diamond modality is that of consistency of a formal theory. Predicate symbols are interpreted as…

The theory of finite and infinitary term rewriting is extensively developed for orthogonal rewrite systems, but to a lesser degree for weakly orthogonal rewrite systems. In this note we present some contributions to the latter case of weak…

It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…

In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…

While large language models (LLMs) are proficient at question-answering (QA), it is not always clear how (or even if) an answer follows from their latent "beliefs". This lack of interpretability is a growing impediment to widespread use of…

We discuss some examples that illustrate the countability of the positive rational numbers and related sets. Techniques include radix representations, Godel numbering, the fundamental theorem of arithmetic, continued fractions, Egyptian…