Cocchiarella’s Formal Ontology and the Paradoxes of Hyperintensionality

This is a critical discussion of Nino B. Cocchiarella’s book “Formal Ontology and Conceptual Realism.” It focuses on paradoxes of hyperintensionality that may arise in formal systems of intensional logic.

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.     

Five Observations Concerning the Intended Meaning of the Intuitionistic Logical Constants

This paper contains five observations concerning the intended meaning of the intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be that of `proof"; (2) Kreisel"s explanations using extra clauses can be significantly simplified; (3) the impredicativity of the definition of can be easily and safely ameliorated; (4) the definition of in terms of `proofs from premises" results in a loss of the inductive character of the definitions of and and (5) the same occurs with the definition of in terms of `proofs with free variables".     

Evolution and Normative Scepticism

It is increasingly common to suggest that the combination of evolutionary theory and normative realism leads inevitably to a general scepticism about our ability to reliably form normative beliefs. In what follows, I argue that this is not the case. In particular, I consider several possible arguments from evolutionary theory and normative realism to normative scepticism and explain where they go wrong. I then offer a more general diagnosis of the tendency to accept such arguments and why this tendency should be resisted.     

Semantic Similarity of Alternatives Fostered by Conversational Negation

Conversational negation often behaves differently from negation as a logical operator: when rejecting a state of affairs, it does not present all members of the complement set as equally plausible alternatives, but it rather suggests some of them as more plausible than others (e.g., “This is not a dog, it is a wolf/*screwdriver”). Entities that are semantically similar to a negated entity tend to be judged as better alternatives (Kruszewski et al., 2016). In fact, Kruszewski et al. (2016) show that the cosine similarity scores between the distributional semantics representations of a negated noun and its potential alternatives are highly correlated with the negated noun-alternatives human plausibility ratings. In a series of cloze tasks, we show that negation likewise restricts the production of plausible alternatives to similar entities. Furthermore, completions to negative sentences appear to be even more restricted than completions to an affirmative conjunctive context, hinting at a peculiarity of negation.     

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].