Related papers: Inner models from extended logics and the Delta-op…
If we replace first order logic by second order logic in the original definition of G\"odel's inner model $L$, we obtain HOD. In this paper we consider inner models that arise if we replace first order logic by a logic that has some, but…
Given a class $\mathcal C$ of models, a binary relation ${\mathcal R}$ between models, and a model-theoretic language $L$, we consider the modal logic and the modal algebra of the theory of $\mathcal C$ in $L$ where the modal operator is…
We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…
In continuous logic, there are plenty of examples of interesting stable metric structures. However, on the other side of the SOP line, there are only a few metric structures where order is relevant, and orders often appear in different…
Information security properties of reactive systems like non-interference often require relating different executions of the system to each other and following them simultaneously. Such hyperproperties can also be useful in other contexts,…
Recent advances in mechanistic interpretability have revealed that large language models (LLMs) develop internal representations corresponding not only to concrete entities but also distinct, human-understandable abstract concepts and…
We introduce a new logic, called \emph{cluster first-order logic}, a restricted fragment of first-order logic specifically designed to study order invariance. An order-invariant formula is one on a vocabulary that contains an order;…
This paper is devoted to systematic studies of some extensions of first-order G\"odel logic. The first extension is the first-order rational G\"odel logic which is an extension of first-order G\"odel logic, enriched by countably many…
Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic…
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
As Large Language Models (LLMs) become increasingly integrated into our daily lives, the potential harms from deceptive behavior underlie the need for faithfully interpreting their decision-making. While traditional probing methods have…
We introduce the $L_!^S$-calculus, a linear lambda-calculus extended with scalar multiplication and term addition, that acts as a proof language for intuitionistic linear logic (ILL). These algebraic operations enable the direct expression…
Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…
Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…
The DL-Lite description logics allow for modeling domain knowledge on top of databases and for efficient reasoning. We focus on metric temporal extensions of DL-Lite_bool and its fragments, and study the complexity of satisfiability. In…
Human logic has gradually shifted from intuition-driven inference to rigorous formal systems. Motivated by recent advances in large language models (LLMs), we explore whether LLMs exhibit a similar evolution in the underlying logical…
The opaque nature of Large Language Models (LLMs) has led to significant research efforts aimed at enhancing their interpretability, primarily through post-hoc methods. More recent in-hoc approaches, such as Concept Bottleneck Models…
Generating rational and generally accurate responses to tasks, often accompanied by example demonstrations, highlights Large Language Model's (LLM's) remarkable In-Context Learning (ICL) capabilities without requiring updates to the model's…
Following the paper~[3] by V\"{a}\"{a}n\"{a}nen and the author, we continue to investigate on the difference between Boolean-valued second-order logic and full second-order logic. We show that the compactness number of Boolean-valued…
Can language models (LMs) learn to faithfully describe their internal computations? Are they better able to describe themselves than other models? We study the extent to which LMs' privileged access to their own internals can be leveraged…