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We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for…
Standpoint extensions of knowledge representation formalisms have been recently introduced as a means to incorporate multi-perspective modelling and reasoning through modal operators that attribute pieces of knowledge to specific entities…
This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers.…
In this short note we observe that the sample complexity of PAC machine learning of various concepts, including learning the maximum (EMX), can be exactly determined when the support of the probability measures considered as models…
We present a new algorithm for general reinforcement learning where the true environment is known to belong to a finite class of N arbitrary models. The algorithm is shown to be near-optimal for all but O(N log^2 N) time-steps with high…
Robust explanations of machine learning models are critical to establish human trust in the models. Due to limited cognition capability, most humans can only interpret the top few salient features. It is critical to make top salient…
We investigate the complexity of bilevel combinatorial optimization with uncertainty in the follower's objective, in a robust optimization approach. We show that the robust counterpart of the bilevel problem under interval uncertainty can…
We give a sufficient condition under which every finite-satisfiable formula of a given PCTL fragment has a model with at most doubly exponential number of states (consequently, the finite satisfiability problem for the fragment is in…
Law codes and regulations help organise societies for centuries, and as AI systems gain more autonomy, we question how human-agent systems can operate as peers under the same norms, especially when resources are contended. We posit that…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
The data-complexity of both satisfiability and finite satisfiability for the two-variable fragment with counting is NP-complete; the data-complexity of both query-answering and finite query-answering for the two-variable guarded fragment…
We make two contributions to the study of polite combination in satisfiability modulo theories. The first contribution is a separation between politeness and strong politeness, by presenting a polite theory that is not strongly polite. This…
The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese (1991). We prove the following problem is decidable: Input: (i) A monadic second…
In this thesis (modal) dependence logic is investigated. It was introduced in 2007 by Jouko V\"a\"aan\"anen as an extension of first-order (resp. modal) logic by the dependence operator =(). For first-order (resp. propositional) variables…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
Explanation methods shed light on the decision process of black-box classifiers such as deep neural networks. But their usefulness can be compromised because they are susceptible to manipulations. With this work, we aim to enhance the…
Given a set of $m$ agents and a set of $n$ items, where agent $A$ has utility $u_{A,i}$ for item $i$, our goal is to allocate items to agents to maximize fairness. Specifically, the utility of an agent is the sum of its utilities for items…