In this paper we investigate those extensions of the bimodal provability logicCSM0 (alias PRL1 or F ) which are subframe logics, i.e. whose general frames are closed under a certain type of substructures. Most bimodal provability logics are in this class. The main result states that all nitely axiomatizable subframe logics containing CSM0 are decidable. We note that, as a rule, interesting syst...

This paper explores many important properties of negations using the neighborhood semantics. We generalize the correspondence between the properties of negations and the conditions on the frames and also establish the duality between distributive lattices with negation and descriptive general negation-neighborhood frames.

This paper presents a semi-automatic method for identifying terms that evoke semantic frames (Fillmore, 1982). The method is tested as a means of identifying lexical units that can be added to existing frames or to new, related frames, using a large corpus on the environment. It is hypothesized that a method based on distributional semantics, which exploits the assumption that words that appear...

In this article two game-theoretically flavored approaches to logic are systematically compared: dialogical logic founded by Paul Lorenzen and Kuno Lorenz, and the game-theoretical semantics of Jaakko Hintikka. For classical Propositional logic and for classical First-order logic, an exact connection between ‘intuitionistic dialogues with hypotheses’ and semantical games is established. Various...

The most obvious bimodal logic generated from unimodal logics L1 and L2 is their fusion, L1 ⊗L2, axiomatized by the theorems of L1 for 1 and of L2 for 2, and by the rules of modus ponens, substitution and necessitation for 1 and for 2. Shehtman introduced the frame product L1×L2, as the logic of the products of certain Kripke frames. Typically, L1 ⊗ L2 ( L1 × L2, e.g. S4⊗ S4 ( S4× S4. Van Benth...

A class of Kripke frames is called modally definable if there is a set of modal formulas such that the class consists exactly of frames on which every formula from that set is valid, i. e. globally true under any valuation. Here, existential definability of Kripke frame classes is defined analogously, by demanding that each formula from a defining set is satisfiable under any valuation. This is...

In this work, we present Paraconsistent Well-Founded Semantics with eXplicit negation (WFSXp) by introducing a frame-based semantics. As far as we know, this is the first time that a declarative approach for WFSXp is effectively characterised in terms of a model theory. Dismissing usual techniques based on immediate consequence operators, our definition depicts WFSXp by minimising models satisf...

This thesis focuses on robust analysis of natural language semantics. A primary bottleneck for semantic processing of text lies in the scarcity of high-quality and large amounts of annotated data that provide complete information about the semantic structure of natural language expressions. In this dissertation, we study statistical models tailored to solve problems in computational semantics, ...

Frame and anti-frame rules have been proposed as proof rules for modular reasoning about programs. Frame rules allow one to hide irrelevant parts of the state during verification, whereas the anti-frame rule allows one to hide local state from the context. We give the first sound model for Charguéraud and Pottier’s type and capability system including both frame and anti-frame rules. The model ...

Frame and anti-frame rules have been proposed as proof rules for modular reasoning about programs. Frame rules allow one to hide irrelevant parts of the state during verification, whereas the anti-frame rule allows one to hide local state from the context. We discuss the semantic foundations of frame and anti-frame rules, and present the first sound model for Charguéraud and Pottier’s type and ...