In 1969, Per Lindstrom proved his celebrated theorem characterising the first-order logic and established criteria for the first-order definability of formal theories for discrete structures. K. J. Barwise, S. Shelah, J. Vaananen and others extended Lindstrom's characterizability program to classes of infinitary logic systems, including a recent paper by M. Dzamonja and J. Vaananen on Karp's chain logic, which satisfies interpolation, undefinability of well-order, and is maximal in the class of logic systems with these properties. The novelty of the chain logic is in its new definition of satisfability. In our paper, we give a framework for Lindstrom's type characterizability of predicate logic systems interpreted semantically in models with objects based on measures (analytic structures). In particular, Hajek's Logic of Integral is redefined as an abstract logic with a new type of Hajek's satisfiability and constitutes a maximal logic in the class of logic systems for describing analytic structures with Lebesgue integrals and satisfying compactness, elementary chain condition, and weak negation.

Aggregates provide a concise way to express complex knowledge. While they are easily understood by humans, formalizing aggregates for answer set programming (ASP) has proven to be challenging . The literature offers many approaches that are not always compatible. One of these approaches, based on Approximation Fixpoint Theory (AFT), has been developed in a logic programming context and has not found much resonance in the ASP-community. In this paper we revisit this work. We introduce the abstract notion of a ternary satisfaction relation and define stable semantics in terms of it. We show that ternary satisfaction relations bridge the gap between the standard Gelfond-Lifschitz reduct, and stable semantics as defined in the framework of AFT. We analyse the properties of ternary satisfaction relations for handling aggregates in ASP programs. Finally, we show how different methods for handling aggregates taken from the literature can be described in the framework and we study the corresponding ternary satisfaction relations.

Characterizing hybrid ASP solving in a generic way is difficult since one needs to abstract from specific theories. Inspired by lazy SMT solving, this is usually addressed by treating theory atoms as opaque. Unlike this, we propose a slightly more transparent approach that includes an abstract notion of a term. Rather than imposing a syntax on terms, we keep them abstract by stipulating only some basic properties. With this, we further develop a semantic framework for hybrid ASP solving and provide aggregate functions for theory variables that adhere to different semantic principles, show that they generalize existing aggregate semantics in ASP and how we can rely on off-the-shelf hybrid solvers for implementation.

The quality criteria of system P have been guiding qualitative uncertain reasoning now for more than two decades. Different semantical approaches have been presented to provide semantics for system P. The aim of the present paper is to investigate the semantical structures underlying system P in more detail, namely, on the level of the models. In particular, we focus on the approach via conditional objects which relies on Boolean intervals, without making any use of qualitative or quantitative information. Indeed, our studies confirm the singular position of conditional objects, but we are also able to establish semantical relationships via novel variants of model theories.