An intensional epistemic logic

One of the fundamental properties inclassical equational reasoning isLeibniz's principle of substitution. Unfortunately, this propertydoes not hold instandard epistemic logic. Furthermore,Herbrand's lifting theorem which isessential to thecompleteness ofresolution andParamodulation in theclassical first order logic (FOL), turns out to be invalid in standard epistemic logic. In particular, unlike classical logic, there is no skolemization normal form for standard epistemic logic. To solve these problems, we introduce anintensional epistemic logic, based on avariation of Kripke's possible-worlds semantics that need not have a constant domain. We show how a weaker notion of substitution through indexed terms can retain the Herbrand theorem. We prove how the logic can yield a satisfibility preserving skolemization form. In particular, we present an intensional principle for unifing indexed terms. Finally, we describe asound andcomplete inference system for a Horn subset of the logic withequality, based onepistemic SLD-resolution.     

A postulate-based analysis of comparative preference statements

There has been a growing interest in the study of preferences for their utility in solving problems related to decision making. Most of the preference representation languages developed in the literature are based on comparative preference statements since they offer a simple and intuitive way for expressing preferences. They can be further interpreted following different semantics, imparting a greater flexibility on how outcomes can be compared. So far the main objective has been to rank-order the set of outcomes given a set of comparative preference statements and one or several semantics. Tackling this problem from a different angle, we look into the behavioural aspects of the preference semantics and statements by attempting to formalise the intuition behind them using postulates studied in preference logics and non-monotonic reasoning. We select the postulates w.r.t. three criteria: coherence, syntax independence and inference. Thus, our analysis provides a means to determine those properties that are satisfied for a given preference semantics.     

The dynamic lexicon in a truth-conditional framework; or how to have Your cake and eat it

A fundamental principle of all truth-conditional approaches to semantics is that the meanings of sentences of natural language can be compositionally specified in terms of truth conditions, where the meanings of the sentences’ parts (words/lexical items) are specified in terms of the contribution they make to such conditions their host sentences possess. Thus, meanings of words fit the meanings of sentences at least to the extent that the stability of what a sentence might mean as specified in a theory is in accord with the stability of what a word might mean as similarly specified. In this paper, I shall be concerned with Ludlow’s (2014) idea that, in fact, there need be no such sympathy between words and sentences. He proposes that we can square what he calls a dynamic lexicon, where word meaning is not stable at all, with a traditional truth-conditional approach of the kind indicated, where sentence meaning is delivered via ‘absolute truth conditions’. I share Ludlow’s aspiration to accommodate dynamic features of word meaning with a truth conditional approach, but not his belief that the marriage is an easy deal. Thus, I shall present a problem for Ludlow’s position and show how resolving this problem leads to an alternative picture of how the meaning of a sentence may be truth-conditionally specified with all relevant dynamic features of the lexicon retained.     

Epistemic Two-Dimensionalism and Empirical Presuppositions

This note argues that Laura Schroeter's [2005] critique of David Chalmers's epistemic two-dimensional semantics is not touched by a reply by Edward Elliott, Kelvin McQueen, and Clas Weber [2013].     

More than belief,but not more than belief and desire

Manuel A. Vásquez’ More Than Belief: A Materialist Theory of Religion paints a rich picture of what a ‘non-reductive materialist framework for the study of religion’ would look like. Although it receives strong motivation from the inability of the predominant meta-approaches of theorizing religion to take seriously a range of materially grounded religious phenomena, it suffers somewhat from a lack of independent and autonomous argumentation. This article explores a convergence between Vásquez’ main points and the basic elements of one of the most influential positions within philosophical semantics – namely the semantic holism of Donald Davidson. Because Davidson's holism (assuming its correctness) provides constraints on all forms of theorizing, the fact that Vásquez’ position, unlike the ones he critiques, conforms to those constraints lends it a degree of rational presumption.     

Parkinson’s disease disrupts both automatic and controlled processing of action verbs

The problem of how word meaning is processed in the brain has been a topic of intense investigation in cognitive neuroscience. While considerable correlational evidence exists for the involvement of sensory-motor systems in conceptual processing, it is still unclear whether they play a causal role. We investigated this issue by comparing the performance of patients with Parkinson’s disease (PD) with that of age-matched controls when processing action and abstract verbs. To examine the effects of task demands, we used tasks in which semantic demands were either implicit (lexical decision and priming) or explicit (semantic similarity judgment). In both tasks, PD patients’ performance was selectively impaired for action verbs (relative to controls), indicating that the motor system plays a more central role in the processing of action verbs than in the processing of abstract verbs. These results argue for a causal role of sensory-motor systems in semantic processing.     

Logic programming as classical inference

We propose a denotational semantics for logic programming based on a classical notion of logical consequence which is apt to capture the main proposed semantics of logic programs. In other words, we show that any of those semantics can be viewed as a relation of the form $T{\models }^{\star }X$ where T is a theory which naturally represents the logic program under consideration together with a set of formulas playing the role of “hypotheses”, in a way which is dictated by that semantics, ${\models }^{\star }$ is a notion of logical consequence which is classical because negation, disjunction and existential quantification receive their classical meaning, and X represents what can be inferred from the logic program, or an intended interpretation of that logic program (such as an answer-set, its well-founded model, etc.). The logical setting we propose extends the language of classical modal logic as it deals with modal operators indexed by ordinals. We make use of two kinds of basic modal formulas: ${\square }_{\alpha }\phi$ which intuitively means that the logical program can generate φ by stage α of the generation process, and ${◇}_{\alpha }{\square }_{\beta }\phi$ with $\alpha >\beta$, which intuitively means that φ can be used as a hypothesis from stage β of the generation process onwards, possibly expecting to confirm φ by stage α (so expecting ${\square }_{\alpha }\phi$ to be generated). This allows us to capture Rondogiannis and Wadge's version of the well-founded semantics [27] where a member of the well-founded model is a closed atom which receives an ordinal truth value of ${\mathtt{true}}_{\alpha }$ or ${\mathtt{false}}_{\alpha }$ for some ordinal α: in our framework, this corresponds to having $T{\models }^{\star }{\square }_{\alpha }\phi$ or $T{\models }^{\star }{\square }_{\alpha }\neg \phi$, respectively, with T being the natural representation of the logic program under consideration and the right set of “hypotheses” as dictated by the well-founded semantics. The framework we present goes much beyond the proposed traditional semantics for logic programming, as it can for instance let us investigate under which conditions a set of hypotheses can be minimal, with each hypothesis being activated as late as possible and confirmed as soon as possible, setting the theoretical foundation to sophisticated ways of making local use of hypotheses in knowledge-based systems, while still being theoretically grounded in a classical notion of logical consequence.