Related papers: $\mathsf{LLF}_{\cal P}$: a logical framework for m…
As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…
The concurrent logical framework CLF is an extension of the logical framework LF designed to specify concurrent and distributed languages. While it can be used to define a variety of formalisms, reasoning about such languages within CLF has…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
Dedukti is a Logical Framework based on the $\lambda$$\Pi$-Calculus Modulo Theory. We show that many theories can be expressed in Dedukti: constructive and classical predicate logic, Simple type theory, programming languages, Pure type…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
A focused proof system provides a normal form to cut-free proofs that structures the application of invertible and non-invertible inference rules. The focused proof system of Andreoli for linear logic has been applied to both the proof…
With the recent success of pre-trained models in NLP, a significant focus was put on interpreting their representations. One of the most prominent approaches is structural probing (Hewitt and Manning, 2019), where a linear projection of…
Modern logics of dependence and independence are based on team semantics, which means that formulae are evaluated not on a single assignment of values to variables, but on a set of such assignments, called a team. This leads to high…
As software systems become more complex, there is an increasing need for new static analyses. Thanks to the declarative style, logic programming is an attractive formalism for specifying them. However, prior work on using logic programming…
The theory of program modules is of interest to language designers not only for its practical importance to programming, but also because it lies at the nexus of three fundamental concerns in language design: the phase distinction,…
We present new induction principles for the syntax of dependent type theories, which we call relative induction principles. The result of the induction principle relative to a functor F into the syntax is stable over the codomain of F. We…
This work studies the proof theory of left (right) skew monoidal closed categories and skew monoidal bi-closed categories from the perspective of non-associative Lambek calculus. Skew monoidal closed categories represent a relaxed version…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
This paper presents a verification framework based on a new class of predicate Constraint Satisfaction Problems called pCSP where constraints are represented as clauses modulo first-order theories over function variables and predicate…
Mechanical proofs by logical relations often involve tedious reasoning about substitution. In this paper, we show that this is not necessarily the case, by developing, in Agda, a proof that all simply typed lambda calculus expressions…
This paper from 2012 is the second in a series of three papers. All three papers deal with interpretability logics and related matters. In the first paper a construction method was exposed to obtain models of these logics. Using this…
Defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning from incomplete and potentially inconsistent knowledge. Defeasible Logic Programming (DeLP) is a defeasible…
Concept-based explanations quantify how high-level concepts (e.g., gender or experience) influence model behavior, which is crucial for decision-makers in high-stakes domains. Recent work evaluates the faithfulness of such explanations by…
Large Language Models (LLMs) achieve strong performance on logical reasoning benchmarks, yet their reliability remains uncertain. Existing evaluations rely on static benchmarks, which fail to assess robustness under logically equivalent…