Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, one-step derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction systems and provide a categorial characterization of the construction. We illustrate the technique in two cases: linear temporal logic versus equational logic; and linear temporal logic versus branching temporal logic. Finally, we lift the synchronization on formulae to the category of logics over consequence systems. Key words: combination of logics, synchronization on formulae, sync...

this paper has been made possible by a gift from the System Development Foundation and was conducted as part of a coordinated research effort with the Center for the Study of Language and Information, Stanford University 30 References

When practicing secure programming, it is important to understand the restrictive influence programmed entities have on the propagation of authority in a program. To precisely model authority propagation in patterns of interacting entities, we present a new formalism Knowledge Behavior Models (KBM). To describe such patterns, we present a new domain specific declarative language SCOLL (Safe Collaboration Language), which semantics are expressed by means of KBMs. To calculate the solutions for the safety problems expressed in SCOLL, we have built SCOLLAR: a model checker and solver based on constraint logic programming. SCOLLAR not only indicates whether the safety requirements are guaranteed by the restricted behavior of the relied-upon entities, but also lists the different ways in which their behavior can be restricted to guarantee the safety properties without precluding their required functionality and (re-)usability. How the tool can help programmers to build reliable components that can safely interact with partially or completely untrusted components is shown in elaborate examples.

This thesis aims to develop a psychologically plausible account of concepts by integrating key insights from philosophy (on the metaphysical basis for concept possession) and psychology (on the mechanisms underlying concept acquisition). I adopt an approach known as informational atomism, developed by Jerry Fodor. Informational atomism is the conjunction of two theses: (i) informational semantics, according to which conceptual content is constituted exhaustively by nomological mind–world relations; and (ii) conceptual atomism, according to which (lexical) concepts have no internal structure. I argue that informational semantics needs to be supplemented by allowing content-constitutive rules of inference (“meaning postulates”). This is because the content of one important class of concepts, the logical terms, is not plausibly informational. And since, it is argued, no principled distinction can be drawn between logical concepts and the rest, the problem that this raises is a general one.

In 1922, Thoraf Skolem published a paper titled "Some remarks on Axiomatized Set Theory". The paper presents a new proof of... This dissertation focuses almost exclusively on the first half of this project -- i.e., the half which tries to expose an initial tension between Cantor's theorem and the Löwenheim-Skolem theorem. I argue that, even on quite naive understandings of set theory and model theory, there is no such tension. Hence, Skolem's Paradox is not a genuine paradox, and there is very little reason to worry about (or even to investigate) the more extreme consequences that are supposed to follow from this paradox. The heart of my...

Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topic-neutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indifferent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought. Though these three notions of formality are by no means equivalent, they are frequently run together. The reason, I argue, is that modern talk of the formality of logic has its source in Kant, and these three notions come together in the context of Kant’s transcendental philosophy. Outside of this context (e.g., in Frege), they can come apart. Attending to this

In the Twentieth Century, Logic and Philosophy of Language are two of the few areas of philosophy in which philosophers made indisputable progress. For example, even now many of the foremost living ethicists present their theories as somewhat more explicit versions of the ideas of Kant, Mill, or Aristotle. In contrast, it would be patently absurd for a contemporary philosopher of language or logician to think of herself as working in the shadow of any figure who died before the Twentieth Century began. Advances in these disciplines make even the most unaccomplished of its practitioners vastly more sophisticated than Kant. There were previous periods in which the problems of language and logic were studied extensively (e.g. the medieval period). But from the perspective of the progress made in the last 120 years, previous work is at most a source of interesting data or occasional insight. All systematic theorizing about content that meets contemporary standards of rigor has been done subsequently. The advances Philosophy of Language has made in the Twentieth Century are of course the result of the remarkable progress made in logic. Few other philosophical disciplines gained as much from the developments in logic as the Philosophy of Language. In the

ABSTRACT. Kolmogorov’s axiomatization of probability includes the familiar ratio formula for conditional probability:

Anumberofdeviantdeductivesystemshavebeenproposedwhichdiffer in some way from classical logic. An influential philosophical interpretation of plurality in logic has been developed by Quine, who introduced the meaningchange thesis, summarized in his "Change of logic, change of subject". We show that if Quine is right about the consequences of his thesis, then the systems of classical logic can only be rejected as unscientific or meaningless, and not refined as inadequate. We show that there are good reasons both for and against his thesis. We argue against Local Pluralism, on the basis that it is incompatible with the universality and normativity of logic. We then assess Beall and Restall’s logical pluralism, which is shown to be not sufficiently fine-grained in that it leads to relativism in logic. We finally introduce Dalla Pozza’s Global Pluralism, where deviant logics are viewed as dealing with specific pragmatic meta-concepts, which are distinct from