We provide new characterizations of the class of regular cost functions (Colcombet 2009) in terms of first-order logic. This extends a classical result stating that each regular language can be defined by a first-order formula over the infinite tree of finite words with a predicate testing words for equal length. Furthermore, we study interpretations for cost logics and use them to provide diff...

Carruthers (2000; 2005) provides a general defence of reductive representationalism about phenomenal consciousness while critiquing first-order theories of the sort proposed by Baars (1988), Tye (1995), Dennett (2001), and others (thereby motivating a form of higher-order account). The present paper defends first-order theories against that attack.

This is a survey of work on set-theoretical invariance criteria for logicality. It begins with a review of the Tarski-Sher thesis in terms, first, of permutation invariance over a given domain and then of isomorphism invariance across domains, both characterized by McGee in terms of definability in the language L ∞,∞. It continues with a review of critiques of the Tarski-Sher thesis, and a prop...

In this paper we introduce Multi-Entity Bayesian Networks (MEBNs) as the means to combine first-order logic with probabilistic inference and facilitate the semantic analysis of Intangible Cultural Heritage (ICH) content. First, we mention the need to capture and maintain ICH manifestations for the safeguarding of cultural treasures. Second, we present the MEBN models and stress their key featur...

This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by providing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fraı̈ssé type theorem. We also give characterizations of elementary classes in equalityfree logic...

We show that the so-called weak Markov’s principle (WMP) which states that every pseudo-positive real number is positive is underivable in T ω :=EHA+AC. Since T ω allows to formalize (at least large parts of) Bishop’s constructive mathematics this makes it unlikely that WMP can be proved within the framework of Bishop-style mathematics (which has been open for about 20 years). The underivabilit...

We describe a model-theoretic approach to ordinal analysis via the finite combinatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with combinatorial properties that, in nonstandard instances, give rise to models of the theory being analyzed. This method is applied to obtai...

This paper investigates the formalization of independence in logic, in particular between quantifiers. We first illustrate that this form of independence plays a role in many fields. A logic that has the possibility to express such a form of independence is Independence Friendly logic (introduced by Hintikka); its semantics is defined by means of strategies in a sequential game. It will be show...

We prove a variant of Läuchli’s completeness theorem for intuitionistic predicate calculus. The formulation of the result relies on the observation (due to Lawvere) that Läuchli’s theorem is related to the logic of the canonical indexing of the atomic topos of Z-sets. We show that the process that transforms Kripke-counter-models into Läuchli-counter-models is (essentially) the inverse image of...

We expand the notion of resplendency to theories of the kind T + p↑, where T is a first-order theory and p↑ expresses that the type p is omitted. We investigate two different formulations and prove necessary and sufficient conditions for countable recursively saturated models of PA. Some of the results in this paper can be found in one of the author’s doctoral thesis [3].