Homogeneity and the illocutionary force of rejection

Homogeneity inferences arise whenever an assertion implies a universal positive (every/both) and its denial implies a universal negative (no/neither). I present an account of homogeneity inferences based on two assumptions which together constrain the behavior of negation: rejection is non-classical, and vacuous models may be omitted (Neglect Zero). If both assumptions are enforced, the only definable negatives are universal (no/neither), predicting the homogeneity gap

The Philippine Challenge to Universal Grammar

Grammatical relations – in particular the relation 'subject of' – and voice are of central concern to any theory of universal grammar. With respect to these phenomena the analysis of Tagalog (and the Philippine languages in general) has turned out to be particularly difficult and continues to be a matter of debate. What traditionally has been called passive voice in these languages […] appears to be so different from voice phenomena in the more familiar Indo-European languages that the term 'focus' was introduced in the late 1950s to underscore its 'exceptional' nature [...]. Furthermore, […] an inflationary use has been made of the term 'ergative' in the last decade; it can thus no longer be assumed that it has an unequivocal and specific meaning in typologizing languages, apart from the technical definition it might be given within a particular framework. But if the Philippine 'focus' constructions are neither passive nor ergative, how else can they be analysed? [...] In this paper a ease will be made for the claim that 'focus' marking should be analysed in terms of orientation, a concept used […] for capturing the difference between English (and, more generally, Indo-European) orientated nominalisations such as 'employ-er' or 'employ-ee', and unorientated nominalisations such as 'employ-ing'. This approach implies that 'focus' marking is derivational rather than inflectional as often presumed in the literature. This is to say that what is typologically conspicuous in Tagalog is not the 'focus' phenomenon per se, since this is very similar to orientated nominalisations in many other languages, but rather the very prominent use of orientated formations (i.e., derivational morphology) in basic clause structure

Logical Semantics and Norms: A Kantian Perspective

It’s widely accepted that normativity is not subject to truth values. The underlying reasoning is that truth values can only be predicated of descriptive statements; normative statements are prescriptive, not descriptive; thus truth value predicates cannot be assigned to normative statements. Hence, deonticity lacks logical semantics. This semantic monism has been challenged over the last decades from a series of perspectives that open the way for legal logics with imperative semantics. In the present paper I will go back to Kant and review his understanding of practical judgments, presenting it as supported by a pluralistic semantics. From this perspective a norm of Law is a logical expression that includes as content a generic description of a possible behavior by a generality of juridical agents, and assigns to that content the assertion of its obligatory character, accompanied by a disincentive for non-compliance. From this perspective legal norms can be syntactically formalized and assigned appropriate semantic values in such terms that they can be incorporated into valid inferential schemes. The consequence is that we can put together legal logics that handle both the phenomenal and the deontic dimensions of legality

PaL Diagrams: A Linear Diagram-Based Visual Language

Linear diagrams have recently been shown to be more effective than Euler diagrams when used for set-based reasoning. However, unlike the growing corpus of knowledge about formal aspects of Euler and Venn diagrams, there has been no formalisation of linear diagrams. To fill this knowledge gap, we present and formalise Point and Line (PaL) diagrams, an extension of simple linear diagrams containing points, thus providing a formal foundation for an effective visual language.We prove that PaL diagrams are exactly as expressive as monadic first-order logic with equality, gaining, as a corollary, an equivalence with the Euler diagram extension called spider diagrams. The method of proof provides translations between PaL diagrams and sentences of monadic first-order logic

Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General

This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment

Model Checking Dynamic-Epistemic Spatial Logic

In this paper we focus on Dynamic Spatial Logic, the extension of Hennessy-Milner logic with the parallel operator. We develop a sound complete Hilbert-style axiomatic system for it comprehending the behavior of spatial operators in relation with dynamic/temporal ones. Underpining on a new congruence we define over the class of processes - the structural bisimulation - we prove the finite model property for this logic that provides the decidability for satisfiability, validity and model checking against process semantics. Eventualy we propose algorithms for validity, satisfiability and model checking

Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories

The computer-mechanization of an ambitious explicit ethical theory, Gewirth's Principle of Generic Consistency, is used to showcase an approach for representing and reasoning with ethical theories exhibiting complex logical features like alethic and deontic modalities, indexicals, higher-order quantification, among others. Harnessing the high expressive power of Church's type theory as a meta-logic to semantically embed a combination of quantified non-classical logics, our work pushes existing boundaries in knowledge representation and reasoning. We demonstrate that intuitive encodings of complex ethical theories and their automation on the computer are no longer antipodes.Comment: 14 page