Related papers: Dependence in Propositional Logic: Formula-Formula…
A key feature of human theory-of-mind is the ability to attribute beliefs to other agents as mentalistic explanations for their behavior. But given the wide variety of beliefs that agents may hold about the world and the rich language we…
Within the formal setting of the Lockean thesis, an agent belief set is defined in terms of degrees of confidence and these are described in probabilistic terms. This approach is of established interest, notwithstanding some limitations…
The AGM recovery postulate says: assume a set of propositions X; assume that it is consistent and that it is closed under logical consequences; remove a belief P from the set minimally, but make sure that the resultant set is again some set…
We find a translation with particularly nice properties from intuitionistic propositional logic in countably many variables to intuitionistic propositional logic in two variables. In addition, the existence of a possibly-not-as-nice…
In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in (Kontinen and Vaananen 2013) and (Hannula 2015). We prove a characterization…
Knowledge bases (KBs) are not static entities: new information constantly appears and some of the previous knowledge becomes obsolete. In order to reflect this evolution of knowledge, KBs should be expanded with the new knowledge and…
Abductive logic programs offer a formalism to declaratively represent and reason about problems in a variety of areas: diagnosis, decision making, hypothetical reasoning, etc. On the other hand, logic program updates allow us to express…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
To build intelligent machine learning systems, there are two broad approaches. One approach is to build inherently interpretable models, as endeavored by the growing field of causal representation learning. The other approach is to build…
The dependency core calculus (DCC), a simple extension of the computational lambda calculus, captures a common notion of dependency that arises in many programming language settings. This notion of dependency is closely related to the…
The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. In order to apply the rationality result of belief dynamics theory to various…
Recent approaches to human concept learning have successfully combined the power of symbolic, infinitely productive rule systems and statistical learning to explain our ability to learn new concepts from just a few examples. The aim of most…
We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…
Revision programming is a formalism to describe and enforce updates of belief sets and databases. That formalism was extended by Fitting who assigned annotations to revision atoms. Annotations provide a way to quantify the confidence…
Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics…
Dependency syntax represents the structure of a sentence as a tree composed of dependencies, i.e., directed relations between lexical units. While in its more general form any such tree is allowed, in practice many are not plausible or are…
The belief revision literature has largely focussed on the issue of how to revise one's beliefs in the light of information regarding matters of fact. Here we turn to an important but comparatively neglected issue: How might one extend a…
We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\alpha), where \alpha is a Boolean variable. Intuitively, with Boolean dependence…
Modern logics of dependence and independence are based on team semantics, which means that formulae are evaluated not on a single assignment of values to variables, but on a set of such assignments, called a team. This leads to high…
First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…