Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

Categorical and Kripke Semantics for Constructive S4 Modal Logic

We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied mainly from type-theoretic and category-theoretic perspectives, but Kripke models for similar systems were studied independently. Here we bring these threads together and prove duality results which show how to relate Kripke models to algebraic models and these in turn to the appropriate categorical models for these logics

Reasoning about actions using description logics with general TBoxes

Abstract. Action formalisms based on description logics (DLs) have recently been introduced as decidable fragments of well-established action theories such as the Situation Calculus and the Fluent Calculus. However, existing DL action formalisms fail to include general TBoxes, which are the standard tool for formalising ontologies in modern description logics. We define a DL action formalism that admits general TBoxes, propose an approach to addressing the ramification problem that is introduced in this way, and perform a detailed investigation of the decidability and computational complexity of reasoning in our formalism.

Correlation of Fractographic Features with Mechanical Properties in Systematically Varied Microstructures of Cu-Strengthened High-Strength Low-Alloy Steel

Fracture is often the culmination of continued deformation. Therefore, it is probable that a fracture surface may contain an imprint of the deformation processes that were operative. In this study, the deformation behavior of copper-strengthened high-strength low-alloy (HSLA) 100 steel has been investigated. Systematic variation of the microstructure has been introduced in the steel through various aging treatments. Due to aging, the coherency, size, shape, and distribution of the copper precipitates were changed, while those of inclusions, carbides, and carbonitrides were kept unaltered. Two-dimensional dimple morphologies, quantified from tensile fracture surfaces, have been correlated to the nature of the variation of the deformation parameters with aging treatment

Branching time logics BTL, U,S , N,N −1(Z)α with operations until and since based on bundles of integer numbers, logical consecutions, deciding algorithms

This paper is intended as an attempt to describe logical consequence in branching time logics. We study temporal branching time logics which use the standard operations Until and Next and dual operations Since and Previous (LTL, as standard, uses only Until and Next). Temporal logics are generated by semantics based on Kripke/Hinttikka structures with linear frames of integer numbers with a single node (glued zeros). For , the permissible branching of the node is limited by α (where 1≤α≤ω). We prove that any logic is decidable w.r.t. admissible consecutions (inference rules), i.e. we find an algorithm recognizing consecutions admissible in . As a consequence, it implies that itself is decidable and solves the satisfiability problem