Related papers: An Expressive Probabilistic Temporal Logic

In this paper we extend the predicate logic introduced in [Beauquier et al. 2002] in order to deal with Semi-Markov Processes. We prove that with respect to qualitative probabilistic properties, model checking is decidable for this logic…

I discuss the meaning of probability in the Everett-Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal…

We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…

Let L be some extension of classical propositional logic. The non-iterated probabilistic logic over L, is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example in PL we can express a…

Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…

Programs increasingly rely on randomization in applications such as cryptography and machine learning. Analyzing randomized programs has been a fruitful research direction, but there is a gap when programs also exploit nondeterminism (for…

This paper aims at providing a comprehensive solution to the archaic open problem: how to define semantics of three-valued modal logic with vivid intuitive picture, convincing philosophical justification as well as versatile practical…

The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…

The handling of probabilities in the form of uncertainty or partial information is an essential task for LLMs in many settings and applications. A common approach to evaluate an LLM's probabilistic reasoning capabilities is to assess its…

In Probabilistic Logic Nilsson uses the device of a probability distribution over a set of possible worlds to assign probabilities to the sentences of a logical language. In his paper Nilsson concentrated on inference and associated…

We present a simple theory explaining the construction and the correctness of an incremental and worst-case optimal decision procedure for modal logic with eventualities. The procedure gives an abstract account of important aspects of…

Possibilistic computation tree Logic (PoCTL) is one kind of branching temporal logic combined with uncertain information in possibility theory, which was introduced in order to cope with the systematic verification on systems with uncertain…

We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…

Probabilistic specifications are fast gaining ground as a tool for statistical modeling of probabilistic systems. One of the main goals of formal methods in this domain is to ensure that specific behavior is present or absent in the system,…

We consider the setting of stochastic multiagent systems modelled as stochastic multiplayer games and formulate an automated verification framework for quantifying and reasoning about agents' trust. To capture human trust, we work with a…

Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…

Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…

Communicating forecast uncertainty effectively is a persistent challenge in predictive endeavours such as weather forecasting. This paper explores the application of possibility theory as a complementary approach to traditional probability…

We study an extension of FO^2[<], first-order logic interpreted in finite words, in which formulas are restricted to use only two variables. We adjoin to this language two-variable atomic formulas that say, `the letter a appears between…

In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…