Related papers: Decidability of All Minimal Models (Revised Versio…

We propose a formal proof of the undecidability of the model checking problem for alternating- time temporal logic under imperfect information and perfect recall semantics. This problem was announced to be undecidable according to a…

To model is to represent. The threshold of decidability defines two epistemological choices: one model (or a finite number of models) suffices for representing the dynamics below the undecidable; above this threshold (defined as…

We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…

How can we find a subset of training samples that are most responsible for a specific prediction made by a complex black-box machine learning model? More generally, how can we explain the model's decisions to end-users in a transparent way?…

We introduce a generalization of the product expansion of a finite semigroup. As an application, we provide an alternative proof of the decidability of pointlike sets for pseudovarieties consisting of semigroups whose subgroups all belong…

The relevance of machine learning (ML) in our daily lives is closely intertwined with its explainability. Explainability can allow end-users to have a transparent and humane reckoning of a ML scheme's capability and utility. It will also…

The group configuration in o-minimal structures gives rise, just like in the stable case, to a transitive action of a type-definable group on a partial type. Because $acl=dcl$ the o-minimal proof is significantly simpler than Hrushovski's…

This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…

We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…

For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…

In recent years, there has been increasing interest in explanation methods for neural model predictions that offer precise formal guarantees. These include abductive (respectively, contrastive) methods, which aim to compute minimal subsets…

In the lambda calculus a term is solvable iff it is operationally relevant. Solvable terms are a superset of the terms that convert to a final result called normal form. Unsolvable terms are operationally irrelevant and can be equated…

We develop a qualitative model of decision making with two aims: to describe how people make simple decisions and to enable computer programs to do the same. Current approaches based on Planning or Decisions Theory either ignore uncertainty…

Despite significant progress in post-hoc explanation methods for neural networks, many remain heuristic and lack provable guarantees. A key approach for obtaining explanations with provable guarantees is by identifying a cardinally-minimal…

Opacity is a generic security property, that has been defined on (non probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an…

Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide…

We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also…

Topological transitivity is a fundamental notion in topological dynamics and is widely regarded as a basic indicator of global dynamical complexity. For general cellular automata, topological transitivity is known to be undecidable. By…

This paper has two parts. In the first one, we prove that an invariant dp-minimal type is either finitely satisfiable or definable. We also prove that a definable version of the (p,q)-theorem holds in dp-minimal theories of small or medium…

Estimates based on 2x2 tables of frequencies are widely used in statistical applications. However, in many cases these tables are incomplete in the sense that the data required to compute the frequencies for a subset of the cells defining…