Well-behaved modal logics

1984 ◽  
Vol 49 (4) ◽  
pp. 1393-1402
Author(s):  
Harold T. Hodes
Keyword(s):  
Modal Logic ◽  
Model Theory ◽  
Classical Model ◽  
Classical Case ◽  
Recursion Theory ◽  
Modal Logics ◽  
Modal Model ◽  
The Right ◽  
Domain Property ◽  
The Way

Much of the literature on the model theory of modal logics suffers from two weaknesses. Firstly, there is a lack of generality; theorems are proved piecemeal about this or that modal logic, or at best small classes of logics. Much of the literature, e.g. [1], [2], and [3], confines attention to structures with the expanding domain property (i.e., if wRu then Ā(w) ⊆ Ā(u)); the syntactic counterpart of this restriction is assumption of the converse Barcan scheme, a move which offers (in Russell's phrase) “all the advantages of theft over honest toil”. Secondly, I think there has been a failure to hit on the best ways of extending classical model theoretic notions to modal contexts. This weakness makes the literature boring, since a large part of the interest of modal model theory resides in the way in which classical model theoretic notions extend, and in some cases divide, in the modal setting. (The relation between α-recursion theory and classical recursion theory is analogous to that between modal model theory and classical model theory. Much of the work in α-recursion theory involved finding the right definitions (e.g., of recursive-in) and separating concepts which collapse in the classical case (e.g. of finiteness and boundedness).)The notion of a well-behaved modal logic is introduced in §3 to make possible rather general results; of course our attention will not be restricted to structures with the expanding domain property. Rather than prove piecemeal that familiar modal logics are well-behaved, in §4 we shall consider a class of “special” modal logics, which obviously includes many familiar logics and which is included in the class of well-behaved modal logics.

Some results in modal model theory

1974 ◽  
Vol 39 (3) ◽  
pp. 496-508 ◽  
Author(s):  
Michael Mortimer
Keyword(s):  
Modal Logic ◽  
Model Theory ◽  
Classical Logic ◽  
Classical Model ◽  
Completeness Theorem ◽  
Strong Completeness ◽  
Barcan Formula ◽  
Weak Completeness ◽  
Modal Model ◽  
Omitting Types

This paper is concerned with extending some basic results from classical model theory to modal logic.In §1, we define the majority of terms used in the paper, and explain our notation. A full catalogue would be excessive, and we cite [3] and [7] as general references.Many papers on modal logic that have appeared are concerned with (i) introducing a new modal logic, and (ii) proving a weak completeness theorem for it. Theorem 1, in §2, in many cases allows us to conclude immediately that a strong completeness theorem holds for such a logic in languages of arbitrary cardinality. In particular, this is true of S4 with the Barcan formula.In §3 we strengthen Theorem 1 for a number of modal logics to deal with the satisfaction of several sets of sentences, and so obtain a realizing types theorem. Finally, an omitting types theorem, generalizing the result for classical logic (see [5]) is proved in §4.Several consequences of Theorem 1 are already to be found in the literature. [2] gives a proof of strong completeness in languages of arbitrary cardinality of various logics without the Barcan formula, and [8] for some logics in countable languages with it. In the latter case, the result for uncountable languages is cited, without proof, in [1], and there credited to Montague. Our proof was found independently.

Quinus ab Omni Nævo Vindicatus1

1997 ◽  
Vol 23 ◽  
pp. 25-65 ◽  
Author(s):  
John P. Burgess
Keyword(s):  
Modal Logic ◽  
Model Theory ◽  
Possible Worlds ◽  
Modal Logics ◽  
Singular Terms ◽  
The 1960S

Today there appears to be a widespread impression that W. V. Quine's notorious critique of modal logic, based on certain ideas about reference, has been successfully answered. As one writer put it some years ago: “His objections have been dead for a while, even though they have not yet been completely buried.” What is supposed to have killed off the critique? Some would cite the development of a new ‘possible-worlds’ model theory for modal logics in the 1960s; others, the development of new ‘direct’ theories of reference for names in the 1970s.These developments do suggest that Quine's unfriendliness towards any formal logics but the classical and indifference towards theories of reference for any singular terms but variables were unfortunate.

The adaptation of design thinking in auditing

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Linda MEIJER-WASSENAAR ◽  
Diny VAN EST
Keyword(s):  
The Netherlands ◽  
Design Thinking ◽  
Public Organizations ◽  
Design Framework ◽  
The Right ◽  
The Way

How can a supreme audit institution (SAI) use design thinking in auditing? SAIs audit the way taxpayers’ money is collected and spent. Adding design thinking to their activities is not to be taken lightly. SAIs independently check whether public organizations have done the right things in the right way, but the organizations might not be willing to act upon a SAI’s recommendations. Can you imagine the role of design in audits? In this paper we share our experiences of some design approaches in the work of one SAI: the Netherlands Court of Audit (NCA). Design thinking needs to be adapted (Dorst, 2015a) before it can be used by SAIs such as the NCA in order to reflect their independent, autonomous status. To dive deeper into design thinking, Buchanan’s design framework (2015) and different ways of reasoning (Dorst, 2015b) are used to explore how design thinking can be adapted for audits.

Memories for the Return? Remembering the Nakba by the First Generation of Palestinian Refugees in Syria

2017 ◽  
Vol 16 (2) ◽  
pp. 177-192 ◽  
Author(s):  
Anaheed Al-Hardan
Keyword(s):  
First Generation ◽  
Palestinian Refugees ◽  
Oslo Accords ◽  
Right Of Return ◽  
Palestinian Refugee ◽  
Temporal And Spatial ◽  
The Right ◽  
Political Realities ◽  
The Way

The 1948 Nakba has, in light of the 1993 Oslo Accords and Palestinian refugee activists' mobilisation around the right of return, taken on a new-found centrality and importance in Palestinian refugee communities. Closely-related to this, members of the ‘Generation of Palestine’, the only individuals who can recollect Nakba memories, have come to be seen as the guardians of memories that are eventually to reclaim the homeland. These historical, social and political realities are deeply rooted in the ways in which the few remaining members of the generation of Palestine recollect 1948. Moreover, as members of communities that were destroyed in Palestine, and whose common and temporal and spatial frameworks were non-linearly constituted anew in Syria, one of the multiples meanings of the Nakba today can be found in the way the refugee communities perceive and define this generation.

Comparative Views on the Right to Vote in International Law

2018 ◽  
Author(s):  
Shai Dothan
Keyword(s):  
Human Rights ◽  
International Law ◽  
National Courts ◽  
European Court ◽  
Right To Vote ◽  
The Right ◽  
Democratic Elections ◽  
The Way

There is a consensus about the existence of an international right to vote in democratic elections. Yet states disagree about the limits of this right when it comes to the case of prisoners’ disenfranchisement. Some states allow all prisoners to vote, some disenfranchise all prisoners, and others allow only some prisoners to vote. This chapter argues that national courts view the international right to vote in three fundamentally different ways: some view it as an inalienable right that cannot be taken away, some view it merely as a privilege that doesn’t belong to the citizens, and others view it as a revocable right that can be taken away under certain conditions. The differences in the way states conceive the right to vote imply that attempts by the European Court of Human Rights to follow the policies of the majority of European states by using the Emerging Consensus doctrine are problematic.

Normative Concepts

2017 ◽  
Author(s):  
Matti Eklund
Keyword(s):  
Positive Answer ◽  
Thick Concepts ◽  
Normative Concepts ◽  
The Right ◽  
The Way

What is it for a concept to be normative? Some possible answers are explored and rejected, among them that a concept is normative if it ascribes a normative property. The positive answer defended is that a concept is normative if it is in the right way associated with a normative use. Among issues discussed along the way are the nature of analyticity, and there being a notion of analyticity—what I call semantic analyticity—such that a statement can be analytic in this sense while failing to be true. Considerations regarding thick concepts and slurs are brought to bear on the issues that come up.

The Inviolability of Diplomatic Agents in the Context of Employment

2017 ◽  
Author(s):  
Lisa Rodgers
Keyword(s):  
Human Rights ◽  
Fair Trial ◽  
European Convention ◽  
Employment Contracts ◽  
Domestic Servants ◽  
Recent Developments ◽  
Diplomatic Immunity ◽  
The Right ◽  
The Way

‘Ordinary’ employment contracts—including those of domestic servants—have been deemed to attract diplomatic immunity because they fall within the scope of diplomatic functions. This chapter highlights the potential for conflict between these forms of immunity and the rights of the employees, and reflects on cases in which personal servants of diplomatic agents have challenged both the existence of immunity and the scope of its application. The chapter examines claims that the exercise of diplomatic immunity might violate the right to a fair trial under Article 6 of the European Convention on Human Rights and the way in which courts have dealt with these issues. The chapter analyses diplomats’ own employment claims and notes that they are usually blocked by the assertion of immunity, but also reflects on more recent developments in which claims had been considered which were incidental to diplomatic employment (eg Nigeria v Ogbonna [2012]).

scholarly journals A Sensibilist Explanation of Imaginative Resistance

2021 ◽  
pp. 1-16
Author(s):  
Nils Franzén
Keyword(s):  
Actual World ◽  
David Hume ◽  
Recent Discussion ◽  
Personal Taste ◽  
Predicates Of Personal Taste ◽  
Imaginative Resistance ◽  
The World ◽  
The Right ◽  
Evaluative Terms ◽  
The Way

Abstract This article discusses why it is the case that we refuse to accept strange evaluative claims as being true in fictions, even though we are happy to go along with other types of absurdities in such contexts. For instance, we would refuse to accept the following statement as true, even in the context of a fiction: (i) In killing her baby, Giselda did the right thing; after all, it was a girl. This article offers a sensibilist diagnosis of this puzzle, inspired by an observation first made by David Hume. According to sensibilism, the way we feel about things settles their evaluative properties. Thus, when confronted with a fictional scenario where the configuration of non-evaluative facts and properties is relevantly similar to the actual world, we refuse to go along with evaluative properties being instantiated according to a different pattern. It is the attitudes we hold in the actual world that fix the extension of evaluative terms, even in nonactual worlds. When engaging with a fiction, we (to some extent) leave our beliefs about what the world is like behind, while taking our emotional attitudes with us into the fiction. To substantiate this diagnosis, this paper outlines a sensibilist semantics for evaluative terms based on recent discussion regarding predicates of personal taste, and explains how, together with standard assumptions about the nature of fictional discourse, it makes the relevant predictions with respect to engagement with fictions.

scholarly journals Transcriptional enhancers and their communication with gene promoters

2021 ◽  
Author(s):  
Helen Ray-Jones ◽  
Mikhail Spivakov
Keyword(s):  
Gene Expression ◽  
Functional Genomics ◽  
Target Genes ◽  
Gene Control ◽  
Gene Promoters ◽  
Joint Effects ◽  
Transcriptional Enhancers ◽  
Quantitative Understanding ◽  
The Right ◽  
The Way

AbstractTranscriptional enhancers play a key role in the initiation and maintenance of gene expression programmes, particularly in metazoa. How these elements control their target genes in the right place and time is one of the most pertinent questions in functional genomics, with wide implications for most areas of biology. Here, we synthesise classic and recent evidence on the regulatory logic of enhancers, including the principles of enhancer organisation, factors that facilitate and delimit enhancer–promoter communication, and the joint effects of multiple enhancers. We show how modern approaches building on classic insights have begun to unravel the complexity of enhancer–promoter relationships, paving the way towards a quantitative understanding of gene control.

scholarly journals FINDING THE LIMIT OF INCOMPLETENESS I

2020 ◽  
Vol 26 (3-4) ◽  
pp. 268-286
Author(s):  
YONG CHENG
Keyword(s):  
Model Theory ◽  
Recursion Theory ◽  
Minimal Degree ◽  
Incompleteness Theorem ◽  
Turing Degree ◽  
Turing Reducibility ◽  
Inseparable Pair

AbstractIn this paper, we examine the limit of applicability of Gödel’s first incompleteness theorem ($\textsf {G1}$ for short). We first define the notion “$\textsf {G1}$ holds for the theory $T$”. This paper is motivated by the following question: can we find a theory with a minimal degree of interpretation for which $\textsf {G1}$ holds. To approach this question, we first examine the following question: is there a theory T such that Robinson’s $\mathbf {R}$ interprets T but T does not interpret $\mathbf {R}$ (i.e., T is weaker than $\mathbf {R}$ w.r.t. interpretation) and $\textsf {G1}$ holds for T? In this paper, we show that there are many such theories based on Jeřábek’s work using some model theory. We prove that for each recursively inseparable pair $\langle A,B\rangle $, we can construct a r.e. theory $U_{\langle A,B\rangle }$ such that $U_{\langle A,B\rangle }$ is weaker than $\mathbf {R}$ w.r.t. interpretation and $\textsf {G1}$ holds for $U_{\langle A,B\rangle }$. As a corollary, we answer a question from Albert Visser. Moreover, we prove that for any Turing degree $\mathbf {0}< \mathbf {d}<\mathbf {0}^{\prime }$, there is a theory T with Turing degree $\mathbf {d}$ such that $\textsf {G1}$ holds for T and T is weaker than $\mathbf {R}$ w.r.t. Turing reducibility. As a corollary, based on Shoenfield’s work using some recursion theory, we show that there is no theory with a minimal degree of Turing reducibility for which $\textsf {G1}$ holds.

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