Related papers: Intuitionistic PUC-Logic for Constructive Counterf…
Explainability is increasingly seen as an essential feature of rule-based smart environments. While counterfactual explanations, which describe what could have been done differently to achieve a desired outcome, are a powerful tool in…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
In many applications, it is important to be able to explain the decisions of machine learning systems. An increasingly popular approach has been to seek to provide \emph{counterfactual instance explanations}. These specify close possible…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
Counterfactuals have been recognized as an effective approach to explain classifier decisions. Nevertheless, they have not yet been considered in the context of clustering. In this work, we propose the use of counterfactuals to explain…
At a first glance the Theory of computation relies on potential infinity and an organization aimed at solving a problem. Under such aspect it is like Mendeleev theory of chemistry. Also its theoretical development reiterates that of this…
This paper investigates the reliability of explanations generated by large language models (LLMs) when prompted to explain their previous output. We evaluate two kinds of such self-explanations - extractive and counterfactual - using three…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
In this paper some proof theory for propositional Lax Logic is developed. A cut free terminating sequent calculus is introduced for the logic, and based on that calculus it is shown that the logic has uniform interpolation. Furthermore, a…
The inverse method is a saturation based theorem proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. Here we apply this method to derive the unprovability…
In this paper, we consider the complexity of propositional proofs of classical and intuitionistic tautologies. In fact, we describe a nondeterministic polynomial-time decision procedure for intuitionistic implicational tautologies. For this…
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…
We present a cut elimination argument that witnesses the conservativity of the compositional axioms for truth (without the extended induction axiom) over any theory interpreting a weak subsystem of arithmetic. In doing so we also fix a…
Uniform interpolation is a strong form of interpolation providing an interpretation of propositional quantifiers within a propositional logic. Pitts' seminal work establishes this property for intuitionistic propositional logic relying on a…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
Several authors have recently defined intuitionistic logic based on team semantics (tIPC). In this paper we provide two alternative approaches to intermediate logics in the team semantics setting. We do this by modifying tIPC with axioms…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…