Journal of Philosophic Logic

  In 1987, Crispin Wright argued that degree-theoretic (fuzzy) solutions to the Sorites paradox fail because the solutions do
 not work when the paradox is restated using a conjunctive major premise. I show that Wright is incorrect: degree-theoretic
 solutions also work when the paradox is stated with a conjunctive major premise.
 
	

  Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced
 and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules (however
 formulated) underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings
 of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try
 to restore the standard readings, for example by adopting sequent rules with multiple conclusions. Another is to explore what
 readings the natural deduction rules do enforce. When the notion of a model of a rule is generalized, it is found that natural
 deduction rules express intuitionistic' readings of their connectives. A third approach is presented here. The intuitionistic
 readings emerge when models of rules are defined globally, but the notion of a local model of a rule is also natural. Using
 this benchmark, natural deduction rules enforce exactly the classical readings of the connectives, while this is not true
 of axiomatic systems. This vindicates the historical motivation for natural deduction rules. One odd consequence of using
 the local model benchmark is that some systems of propositional logic are not complete for the semantics that their rules
 express. Parallels are drawn with incompleteness results in modal logic to help make sense of this.
 
	

  Routley-Meyer type ternary relational semantics are defined for relevant logics including Routley and Meyer's basic logic
 B plus the reductio rule  and the disjunctive syllogism. Standard relevant logics such as E and R (plus γ) and Ackermann's logics of ˜strenge Implikation' Π and Π² are among the logics considered.
 
	

  The Lambek-Grishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of
 type-forming operations (product and residual left and right division) with a dual family: coproduct, left and right difference.
 Interaction between these two families is provided by distributivity laws. These distributivity laws have pleasant invariance
 properties: stability of interpretations for the Curry-Howard derivational semantics, and structure-preservation at the syntactic
 end. The move to symmetry thus offers novel ways of reconciling the demands of natural language form and meaning.
 
	

  In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ˜natural logic'. His paper makes
 a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond
 to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading
 difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e.
 separately for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise
 globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes
 of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on
 the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan's view that
 natural logic is ˜natural'.
 
	

  This paper asks why information should ever be expressed vaguely, re-assessing some previously proposed answers to this question
 and suggesting some new ones. Particular attention is paid to the benefits that vague expressions can have in situations where
 agreement over the meaning of an expression cannot be taken for granted. A distinction between two different versions of the
 above-mentioned question is advocated. The first asks why human languages contain vague expressions, the second question asks when and why a speaker should choose a vague expression when communicating
 with a hearer. While the former question is purely theoretical, the latter has practical implications for the computational
 generation of utterances in Natural Language Generation (NLG).
 
	

  This article takes off from Johan van Benthem's ruminations on the interface between logic and cognitive science in his position
 paper Logic and reasoning: Do the facts matter?'. When trying to answer Van Benthem's question whether logic can be fruitfully
 combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social
 cognition, including attributions such as Bob knows that Alice knows that he wrote a novel under pseudonym'. For intelligent
 interaction, it is important that the participants recursively model the mental states of other agents. Otherwise, an international
 negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software
 agent may depend on a teammate's action that never materializes. First a survey is presented of past and current research
 on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people
 actually reason about each other's knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive
 science productively work together to construct more realistic models of human reasoning about other minds? The paper ends
 with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social
 reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and
 agent-based evolutionary models.
 
	

  While logical theories of information attitudes, such as knowledge, certainty and belief, have flourished in the past two
 decades, formalization of other facets of rational behavior have lagged behind significantly. One intriguing line of research
 concerns the concept of intention. I will discuss one approach to tackling the notion within a logical framework, based on
 a database perspective.
 
	

Special Issue on the Occasion of Johan van Benthem's 60th Birthday'Editorial
	

  Soames (Philos Top 15:44“87, 1987, J Philos Logic 37:267“276, 2008) has argued that propositions cannot be sets of truth-supporting circumstances. This argument is criticized for assuming
 that various singular terms are directly referential when in fact there are good grounds to doubt this.
 
	

  Nelson Goodman's new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory
 of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent
 predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant
 characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar
 to Popper's notion of degrees of testability is linked to minimizing expected predictive error. In contrast, formal learning
 theory appeals to Ockham's razor, which it justifies by reference to the goal of enhancing efficient convergence to the truth.
 In this essay, I show that, despite their differences, statistical and formal learning theory yield precisely the same result
 for a class of inductive problems that I call strongly VC ordered, of which Goodman's riddle is just one example.
 
	

  The Routley-Meyer relational semantics for relevant logics is extended to give a sound and complete model theory for many
 propositionally quantified relevant logics (and some non-relevant ones). This involves a restriction on which sets of worlds
 are admissible as propositions, and an interpretation of propositional quantification that makes ˆ‰pA true when there is some true admissible proposition that entails all p-instantiations of A. It is also shown that without the admissibility qualification many of the systems considered are semantically incomplete,
 including all those that are sub-logics of the quantified version of Anderson and Belnap's system E of entailment, extended
 by the mingle axiom and the Ackermann constant t. The incompleteness proof involves an algebraic semantics based on atomless complete Boolean algebras.
 
	

  In recent years, much work has been dedicated by logicians, computer scientists and economists to understanding awareness,
 as its importance for human behaviour becomes evident. Although several logics of awareness have been proposed, little attention
 has been explicitly dedicated to change in awareness. However, one of the most crucial aspects of awareness is the changes
 it undergoes, which have countless important consequences for knowledge and action. The aim of this paper is to propose a
 formal model of awareness change, and to derive from it logics of awareness change. In the first part of the paper, the model
 of epistemic states of bounded agents proposed in Hill (Stud Log 89(1):81“109, 2008a) is extended with operations modelling awareness change. In the second part of the paper, it is shown how this model naturally
 extends the standard' logic of awareness to yield a logic of awareness change.
 
	

  In response to the liar's paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. (Martin and Woodruff independently developed this semantics,
 but not to the same extent as Kripke.) Kripke's work suggests a number of related fixed-point theories of truth for such languages.
 Gupta and Belnap develop their revision theory of truth in contrast to the fixed-point theories. The current paper considers three natural ways to compare the various resulting
 theories of truth, and establishes the resulting relationships among these theories. The point is to get a sense of the lay
 of the land amid a variety of options. Our results will also provide technical fodder for the methodological remarks of the
 companion paper to this one.
 
	

  Surrender; therefore, surrender or fight' is apparently an argument corresponding to an inference from an imperative to an
 imperative. Several philosophers, however (Williams 1963; Wedeking 1970; Harrison 1991; Hansen 2008), have denied that imperative
 inferences exist, arguing that (1) no such inferences occur in everyday life, (2) imperatives cannot be premises or conclusions
 of inferences because it makes no sense to say, for example, since surrender' or it follows that surrender or fight', and
 (3) distinct imperatives have conflicting permissive presuppositions (surrender or fight' permits you to fight without surrendering,
 but surrender' does not), so issuing distinct imperatives amounts to changing one's mind and thus cannot be construed as
 making an inference. In response I argue inter alia that, on a reasonable understanding of ˜inference', some everyday-life
 inferences do have imperatives as premises and conclusions, and that issuing imperatives with conflicting permissive presuppositions
 does not amount to changing one's mind.
 
	

  The Substitution Anomaly is the failure of intuitively coreferential expressions of the corresponding forms that S' and the proposition that S'
 to be intersubstitutable salva veritate under certain ˜selective' attitudinal verbs that grammatically accept both sorts of terms as complements. The Substitution
 Anomaly poses a direct threat to the basic assumptions of Millianism, which predict the interchangeability of that S' and
 the proposition that S'. Jeffrey King has argued persuasively that the most plausible Millian solution is to treat the selective
 attitudinal verbs as lexically ambiguous, having distinct meanings associated with the different sorts of complement terms. In opposition this approach, I argue that
 there are independent reasons for maintaining the univocality of these verbs and that this can be done while accommodating
 the Substitution Anomaly and without sacrificing the transparency of the relevant attitude ascriptions. In particular, I show
 how, by employing an extended version of Edward Zalta's system of intensional logic for abstract objects, one can construct
 for a regimented fragment „ of English containing the relevant vocabulary a semantical theory „‘ which (a) treats „'s selective
 attitudinal verbs as univocal, (b) regards genuine terms as occurring transparently under such verbs in sentences of „, and
 yet (c) predicts the occurrence of the Substitution Anomaly in „.
 
	

  Deflationists say that the equivalence between ˜p is true' and p is all there is to the meaning of ˜true'. Use' theories
 generally construe meaning as acceptance conditions. I argue: (i) there are certain obvious objections to a deflationary theory
 of truth so formulated; but (ii) they can be overcome if we employ a graded notion of use, i.e. a notion of assertability;
 but (iii) there appear to be certain further difficulties which cannot be overcome in this way.
 
	

  This note explains an error in Restall's ˜Simplified Semantics for Relevant Logics (and some of their rivals)' (Restall, J
 Philos Logic 22(5):481“511, 1993) concerning the modelling conditions for the axioms of assertion A †’ ((A †’ B) †’ B) (there called c6) and permutation (A †’ (B †’ C)) †’ (B †’ (A †’ C)) (there called c7). We show that the modelling conditions for assertion and permutation proposed in ˜Simplified Semantics' overgenerate. In
 fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism.
 The semantics provides for no models of R in which the base point' is inconsistent. This problem is not restricted to ˜Simplified Semantics.' The techniques
 of that paper are used in Graham Priest's textbook An Introduction to Non-Classical Logic (Priest, 2001), which is in wide circulation: it is important to find a solution. In this article, we explain this result, diagnose the
 mistake in ˜Simplified Semantics' and propose two different corrections.
 
	

  Several authors proposed to devise logical structures for Natural Language (NL) semantics in which noun phrases yield referential
 terms rather than standard Generalized Quantifiers. In this view, two main problems arise: the need to refer to the maximal
 sets of entities involved in the predications and the need to cope with Independent Set (IS) readings, where two or more sets
 of entities are introduced in parallel. The article illustrates these problems and their consequences, then presents an extension
 of the proposal made in Sher (J Philos Logic 26:1“43, 1997) in order to properly represent the meaning of IS readings involving NL quantifiers. The solution proposed here allows to
 uniformly deal with both standard linear and IS readings, regardless of their actual existence in NL or quantifiers' monotonicity.
 Sentences featuring nested quantifications are particularly problematic. By avoiding parallel nested quantification in the
 formulae, the proper true values are achieved.
 
	

  In this essay, I propose an analysis of Quine's example 'Giorgione was so-called because of his size', grounded on the idea
 of an obstinate demonstrative. In the first sections, I discuss the advantages and drawbacks of the demonstrative and logophoric
 treatments of ˜so called', I highlight certain parallelisms with Davidson's paratactic view of quotation, and I introduce
 independent considerations in favor of the idea of an obstinate demonstrative. In the second half of my essay, I apply this
 notion to Quine's example, and I discuss its consequences with respect to the principle of substitutivity of coreferential
 singular terms.