Coalgebraic modal logic serves as a unifying framework to study a wide range of modal logics beyond the relational realm, including probabilistic and graded logics as well as conditional logics and logics based on neighbourhoods and games. Coalgebraic predicate logic (CPL), a generalization of a neighbourhoodbased first-order logic introduced by Chang, has been identified as a natural first-ord...

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both...

In this paper, we present an alternative interpretation of propositional inquisitive logic as epistemic knowing how. our setting, formula $\alpha$ being supported by a state is formalized "knowing how to resolve $\alpha$" (more colloquially, true") holds on the S5 model corresponding state. Based interpretation, use dynamic with both know-how and know-that operators capture information behind i...

This paper examines various propositional logics in which the dynamic implication connective ⇒ (discussed in Groenendijk and Stokhof’s (1992) Dynamic Predicate Logic and Kamp’s (1981) Discourse Representation Theory) plays the central role. Our approach is modal: we view ⇒ as a binary modal operator in a two dimensional modal logic. Two dimensional modal logics are systems in which formulas are...

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both...

We give a technique to construct a final coalgebra in which each element is a set of formulas of modal logic. The technique works for both the finite and the countable powerset functors. Starting with an injectively structured, corecursive algebra, we coinductively obtain a suitable subalgebra called the “co-founded part”. We see – first with an example, and then in the general setting of modal...

We define a procedure for translating given first-order formula to an equivalent modal formula, if one exists, by using tableau-based bisimulation invariance test. A previously developed tableau tests of and therefore whether that is the standard translation some formula. Using closed as starting point, we show how can be effectively obtained.

In this paper we show that first-order temporal logics form a proper expressiveness hierarchy with respect to dimensionality and quantifier depth of temporal connectives. This result resolves (negatively) the open question concerning the existence of an expressively complete first-order temporal logic, even when allowing multi-dimensional temporal connectives.

These notes were written by Wang Yafeng following a course of three intensive lectures on classical themes in mathematical modal logic given by Johan van Benthem in the Berkeley-Stanford Logic Circle, San Francisco, May 2015. Some of this material was collected in the monograph van Benthem [13], [16], other parts come from later publications. We will provide some references to further relevant ...

Separation logic is a concise method for specifying programs that manipulatedynamically allocated storage. Partially inspired by separation logic, Implicit DynamicFrames has recently been proposed, aiming at first-order tool support. In this paper,we precisely connect the semantics of these two logics. We define a logic whose syntaxsubsumes both that of a standard separation log...