Related papers: Computing Theory Prime Implicates in Modal Logic

Complexity theory is a useful tool to study computational issues surrounding the elicitation of preferences, as well as the strategic manipulation of elections aggregating together preferences of multiple agents. We study here the…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

This work introduces a framework for quantifying the information content of logical propositions through the use of implication hypergraphs. We posit that a proposition's informativeness is primarily determined by its relationships with…

Two different approaches to dealing with probabilistic knowledge are examined -models and inductive inference. Examples of the first are: influence diagrams [1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second are:…

Scaling laws have allowed Pre-trained Language Models (PLMs) into the field of causal reasoning. Causal reasoning of PLM relies solely on text-based descriptions, in contrast to causal discovery which aims to determine the causal…

In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…

The concept of causality has a controversial history. The question of whether it is possible to represent and address causal problems with probability theory, or if fundamentally new mathematics such as the do-calculus is required has been…

Systems thinking provides us with a way to model the algorithmic fairness problem by allowing us to encode prior knowledge and assumptions about where we believe bias might exist in the data generating process. We can then encode these…

Matching plays a vital role in the rational allocation of resources in many areas, ranging from market operation to people's daily lives. In economics, the term matching theory is coined for pairing two agents in a specific market to reach…

Uniform interpolation is the property that, for any formula and set of atoms, there exists the strongest consequence omitting those atoms. It plays a central role in knowledge representation and reasoning tasks such as knowledge update and…

Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…

We start a systematic investigation of the size of Craig interpolants, uniform interpolants, and strongest implicates for (quasi-)normal modal logics. Our main upper bound states that for tabular modal logics, the computation of strongest…

We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…

First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…

Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…

Time series prediction is of great significance in many applications and has attracted extensive attention from the data mining community. Existing work suggests that for many problems, the shape in the current time series may correlate an…

Probabilistic justification logic is a modal logic with two kind of modalities: probability measures and explicit justification terms. We present a tableau procedure that can be used to decide the satisfiability problem for this logic in…

We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…

Explicit theory axioms are added by a saturation-based theorem prover as one of the techniques for supporting theory reasoning. While simple and effective, adding theory axioms can also pollute the search space with many irrelevant…