Two Reformulations of the Verificationist Thesis in Epistemic Temporal Logic that Avoid Fitch’s Paradox

1) We will begin by offering a short introduction to Epistemic Logic and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will proceed to presenting three Epistemic Temporal logical frameworks creat‑ ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL (Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (Temporal Public Announcement Logic with Labeled Past Operators). We will show how Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze his argument on why this version of it is immune from paradox. (3) Edgington (1985) offered an interpretation of the Verificationist Thesis that blocks Fitch’s paradox and we will propose a way to formulate it in a TAPAL‑based lan‑ guage. The language we will use is a combination of TAPAL and TPAL+P ! with an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑ ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑ tive semantics for this language. We will investigate whether the tentative re‑ formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from paradox and adequate to Edgington’s ideas on how „all truths are knowable“ should be interpreted

Tool support for reasoning in display calculi

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calculus D.EAK of dynamic epistemic logic. Second, we provide embeddings of the calculus in the theorem prover Isabelle for formalising proofs about D.EAK. As a case study we show that the solution of the muddy children puzzle is derivable for any number of muddy children. Third, there is a set of meta-tools, that allows us to adapt the tool for a wide variety of user defined calculi

Strategic considerations in monetary policy with private information: can secrecy be avoided?

Monetary policy

Money supply announcements, forward interest rates and budget deficits

Interest rates ; Money supply ; Budget deficits ; Inflation (Finance)

Navigating Religious Rights of Teachers and Students: Establishment, Accommodation, Neutrality, or Hostility?

Despite the notion that First Amendment rights are established, valued, and respected in the United States, there continues to be confusion in public schools that leads to legal conflict over issues associated with freedoms of speech and expression, especially as they relate to religious issues. Navigating the religious rights of teachers and students can be a precarious undertaking, as administrators’ decisions regarding the expression of religious beliefs continue to be highlighted in the media and many times are resolved in the court system at great expense to school districts. The purpose of this article is to clarify religious rights issues for school administrators and school boards. What actions risk violating the establishment clause or expressing hostility toward religion? When and how is religion best accommodated while neutrality is maintained? This study traces court decisions and laws that serve to guide religious rights policies and practices. It also examines recent conflicts and the legal organizations whose mission it is to address First Amendment violations

Strategic considerations in monetary policy with private information: can secrecy be avoided?

Monetary policy

The Linking of Collective Decisions and Efficiency

For groups that must make several decisions of similar form, we define a simple and general mechanism that is designed to promote social efficiency. The mechanism links the various decisions by forcing agents to budget their representations of preferences so that the frequency of preferences across problems conforms to the underlying distribution of preferences. We show that as the mechanism operates over a growing number decisions, the welfare costs of incentive constraints completely disappear. In addition, as the number of decisions being linked grows, a truthful strategy is increasingly successful and secures the efficient utility level for an agent.linking decisions, mechanism design, incentives, incentive compatibility, bundling