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In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability…
This paper is composed of two main results concerning chains of infinite order which are not necessarily continuous. The first one is a decomposition of the transition probability kernel as a countable mixture of unbounded probabilistic…
The entailment problem $\varphi \models \psi$ in Separation Logic \cite{IshtiaqOHearn01,Reynolds02}, between separated conjunctions of equational ($x \iseq y$ and $x \not\iseq y$), spatial ($x \mapsto (y_1,\ldots,y_\rank)$) and predicate…
In this research, new concepts of existential granules that determine themselves are invented, and are characterized from algebraic, topological, and mereological perspectives. Existential granules are those that determine themselves…
Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising…
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
For three natural classes of dynamic decision problems; 1. additively separable problems, 2. discounted problems, and 3. discounted problems for a fixed discount factor; we provide necessary and sufficient conditions for one sequential…
We consider the problem of monitoring a Linear Time Logic (LTL) specification that is defined on infinite paths, over finite traces. For example, we may need to draw a verdict on whether the system satisfies or violates the property "p…
Contextual online decision-making problems with constraints appear in a wide range of real-world applications, such as adaptive experimental design under safety constraints, personalized recommendation with resource limits, and dynamic…
Interpretable rationales for model predictions are crucial in practical applications. We develop neural models that possess an interpretable inference process for dependency parsing. Our models adopt instance-based inference, where…
We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…
Moving beyond the dualistic view in AI where agent and environment are separated incurs new challenges for decision making, as calculation of expected utility is no longer straightforward. The non-dualistic decision theory literature is…
The \emph{Entscheidungsproblem}, or the classical decision problem, asks whether a given formula of first-order logic is satisfiable. In this work, we consider an extension of this problem to regular first-order \emph{theories}, i.e.,…
The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable…
In decentralized stochastic control (or stochastic team theory) and game theory, if there is a pre-defined order in a system in which agents act, the system is called \textit{sequential}, otherwise it is non-sequential. Much of the…
Decision mining enables the discovery of decision rules from event logs or streams, and constitutes an important part of in-depth analysis and optimisation of business processes. So far, decision mining has been merely applied in an ex-post…
We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula phi(X,x) that is positive in X, it is decidable whether the…