Probabilistic Approach to Epistemic Modals in the Framework of Dynamic Semantics

In dynamic semantics meaning of a statement is not equated with its truth conditions but with its context change potential. It has also been claimed that dynamic framework can automatically account for certain paradoxes that involve epistemic modals, such as the following one: it seems odd and incoherent to claim: (1) “It is raining and it might not rain”, whereas claiming (2) “It might not rain and it is raining” does not seem equally odd (Yalcin, 2007). Nevertheless, it seems that it cannot capture the fact that statement (2) seems odd as well, even though not as odd as the statement (1) (Gauker, 2007). I will argue that certain probabilistic extensions to the dynamic model can account for this subtlety of our linguistic intuitions and represent if not an improved than at least an alternative framework for capturing the way contexts are updated and beliefs revised with uncertain information.Numer został przygotowany przy wsparciu Ministerstwa Nauki i Szkolnictwa Wyższego

Statistical relational learning with soft quantifiers

Quantification in statistical relational learning (SRL) is either existential or universal, however humans might be more inclined to express knowledge using soft quantifiers, such as ``most'' and ``a few''. In this paper, we define the syntax and semantics of PSL^Q, a new SRL framework that supports reasoning with soft quantifiers, and present its most probable explanation (MPE) inference algorithm. To the best of our knowledge, PSL^Q is the first SRL framework that combines soft quantifiers with first-order logic rules for modelling uncertain relational data. Our experimental results for link prediction in social trust networks demonstrate that the use of soft quantifiers not only allows for a natural and intuitive formulation of domain knowledge, but also improves the accuracy of inferred results

Model checking Quantitative Linear Time Logic

This paper considers QLtl, a quantitative analagon of Ltl and presents algorithms for model checking QLtl over quantitative versions of Kripke structures and Markov chains

Quantified Markov logic networks

Markov Logic Networks (MLNs) are well-suited for expressing statistics such as “with high probability a smoker knows another smoker” but not for expressing statements such as “there is a smoker who knows most other smokers”, which is necessary for modeling, e.g. influencers in social networks. To overcome this shortcoming, we study quantified MLNs which generalize MLNs by introducing statistical universal quantifiers, allowing to express also the latter type of statistics in a principled way. Our main technical contribution is to show that the standard reasoning tasks in quantified MLNs, maximum a posteriori and marginal inference, can be reduced to their respective MLN counterparts in polynomial time