Related papers: Preliminary Notes on Termination and Non-Terminati…
Humans and animals have the ability to reason and make predictions about different courses of action at many time scales. In reinforcement learning, option models (Sutton, Precup \& Singh, 1999; Precup, 2000) provide the framework for this…
We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we…
We survey the different properties of an intuitive notion of redundancy, as a function of the precise semantics given to the notion of partial implication. The final version of this survey will appear in the Proceedings of the Int. Conf.…
This is an overview and a preview of the theory of "mixed motives of level 1" explaining some results, projects, ideas and indicating a bunch of problems.
In this work, we consider the problem of autonomously discovering behavioral abstractions, or options, for reinforcement learning agents. We propose an algorithm that focuses on the termination condition, as opposed to -- as is common --…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
We use the notion of a partial action of a monoid to introduce a generalization of automata, which we call "a preautomaton". We study properties of preautomata and of languages recognized by preautomata.
An earlier paper gives an account of a quest for a satisfactory formalization of the classical informal notion of an algorithm. That notion only covers algorithms that are deterministic and non-interactive. In this paper, an attempt is made…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
In this paper, we develop new optional stopping theorems for scenarios where the stopping rules are defined by bounded continuity regions. Moreover, we establish a wide variety of inequalities on the supremums and infimums of functions of…
A semantic tableau method, called an argumentation tableau, that enables the derivation of arguments, is proposed. First, the derivation of arguments for standard propositional and predicate logic is addressed. Next, an extension that…
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
We present a syntactic abstraction method to reason about first-order modal logics by using theorem provers for standard first-order logic and for propositional modal logic.
To develop a full abstract denotational model of a process language based on prebisimulation preorder, its behavioural semantics has two problems: (1) Two processes related by a standard denotational interpretation afford the same finite…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
In this article we determine the implicational fragments of most of the known subintuitionistic logics.
In this paper, we define two particular forms of non-termination, namely loops and binary chains, in an abstract framework that encompasses term rewriting and logic programming. The definition of loops relies on the notion of compatibility…
This article examines the interpretation of the LTL temporal operators over finite and infinite sequences. This is used as the basis for deriving a sound and complete axiomatization for Caret, a recent temporal logic for reasoning about…