A logic for deontic dilemmas

The possibility of deontic dilemmas poses a significant problem for deontic logic. Here I review some proposals to resolve this problem, and then offer a new account. This is a simple modification of standard deontic logic that enables the system to accommodate deontic dilemmas without inconsistency and without deontic explosion, while at the same time accounting for the range of genuinely valid inferences.     

A conditional logic for abduction

We propose a logic of abduction that (i) provides an appropriate formalization of the explanatory conditional, and that (ii) captures the defeasible nature of abductive inference. For (i), we argue that explanatory conditionals are non-classical, and rely on Brian Chellas’s work on conditional logics for providing an alternative formalization of the explanatory conditional. For (ii), we make use of the adaptive logics framework for modeling defeasible reasoning. We show how our proposal allows for a more natural reading of explanatory relations, and how it overcomes problems faced by other systems in the literature.     

A tense logic for boethius

An interpretation in modal and tense logic is proposed for Boethius's reconciliation of God's foreknowledge with human freedom from The consolation of philosophy, Book V. The interpretation incorporates a suggestion by Paul Spade that God's special status in time be explained as a restriction of God's knowledge to eternal sentences. The argument proves valid, and the seeming restriction on omnipotence is mitigated by the very strong expressive power of eternal sentences.     

A base logic for default reasoning

Based on a close study of benchmark examples in default reasoning, such as Nixon Diamond, Penguin Principle, etc., this paper provides an in depth analysis of the basic features of default reasoning. We formalize default inferences based on Modus Ponens for Default Implication, and mark the distinction between “local inferences” (to infer a conclusion from a subset of given premises) and “global inferences” (to infer a conclusion from the entire set of given premises). These conceptual analyses are captured by a formal semantics that is built upon the set-selection function technique. A minimal logic system M of default reasoning that accommodates Modus Ponens for Default Implication and suitable for local inferences is proposed, and its soundness is proved. __________ Translated from Zhexue Yanjiu 哲学研究 (Philosophical Studies), 2003 (special issue) by Ye Feng     

A logic for epistemic two-dimensional semantics

Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also describe some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem.     

A gentzen system for conditional logic

Conditional logic is the deductive system , where is the set of propositional connectives {, ,} and is the structural finitary consequence relation on the absolutely free algebra that preserves degrees of truth over the structure of truth values C, . HereC is the non-commutative regular extension of the 2-element Boolean algebra to 3 truth values {t, u, f}, andf<u<t. In this paper we give a Gentzen type axiomatization for conditional logic.Presented byJan Zygmunt     

A utilitarian semantics for deontic logic

I am idebted to members of the Wellington Logic Seminar for useful discussions of work of which this essay forms part, in particular to M. J. Cresswell for comments in the earlier stages of the investigation and to R. I. Goldblatt who suggested the definition ofB _infD ^supu and made numerous other suggestions.     

A logic for diffusion in social networks

This paper introduces a general logical framework for reasoning about diffusion processes within social networks. The new “Logic for Diffusion in Social Networks” is a dynamic extension of standard hybrid logic, allowing to model complex phenomena involving several properties of agents. We provide a complete axiomatization and a terminating and complete tableau system for this logic and show how to apply the framework to diffusion phenomena documented in social networks analysis.     

A positive information logic for inferential information

Performing an inference involves irreducibly dynamic cognitive procedures. The article proposes that a non-associative information frame, corresponding to a residuated pogroupoid, underpins the information structure involved. The argument proceeds by expounding the informational turn in logic, before outlining the cognitive actions at work in deductive inference. The structural rules of Weakening, Contraction, Commutation, and Association are rejected on the grounds that they cause us to lose track of the information flow in inferential procedures. By taking the operation of information application as the primary operation, the fusion connective is retained, with commutative failure generating a double implication. The other connectives are rejected.