Journal of Logic Language and Information

  The neutralization of contrasts in form or meaning that is sometimes observed in language production and comprehension is
 at odds with the classical view that language is a systematic one-to-one pairing of forms and meanings. This special issue
 is concerned with patterns of forms and meanings in language. The papers in this special issue arose from a series of workshops
 that were organized to explore variants of bidirectional Optimality Theory and Game Theory as models of the interplay between
 the speaker's and the hearer's perspective.
 
 
	

  This study accounts for the observed patterns of variation and ambiguity in the expression and interpretation of aspect in
 bare habitual statements in Polish in the framework of Bouma's (2008) recent version of stratified bi-directional Optimality Theory (OT).
 
 
	

  A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid
 if and only if it is provable in the calculus.
 
 
	

  Young French children freely produce subject pronouns by the age of 2. However, by age 2 and a half they fail to interpret
 3rd person pronouns in an experimental setting designed to select a referent among three participants (speaker, hearer, and
 other). No such problems are found with 1st and 2nd person pronouns. We formalize our analysis of these empirical results
 in terms of direction-sensitive optimizations, showing that uni-directionality of optimization, when combined with non-adult-like
 constraint rankings, explains the general acquisition pattern of 3rd person pronouns. Building on a specific analysis of assigning
 3rd person reference by computing over alternatives (Heim 1991), we show that adult interpretation does not require bidirectional OT although it is fully compatible with it. What matters
 for comprehension in the domain investigated here is constraint ranking.
 
 
	

  A proposal for an objective interpretation of probability is introduced and discussed: probabilities as deriving from ranges
 in suitably structured initial-state spaces. Roughly, the probability of an event on a chance trial is the proportion of initial
 states that lead to the event in question within the space of all possible initial states associated with this type of experiment,
 provided that the proportion is approximately the same in any not too small subregion of the space. This I would like to call
 the natural-range conception' of probability. Providing a substantial alternative to frequency or propensity accounts of
 probability in a deterministic setting, it is closely related to the so-called method of arbitrary functions'. It is explicated,
 confronted with certain problems, and some ideas how these might be overcome are sketched and discussed.
 
 
	

  We reopen the investigation into the formal and conceptual relationship between bidirectional optimality theory (Blutner in
 J Semant 15(2):115“162, 1998, J Semant 17(3):189“216, 2000) and game theory. Unlike a likeminded previous endeavor by Dekker and van Rooij (J Semant 17:217“242, 2000), we consider signaling games not strategic games, and seek to ground bidirectional optimization once in a model of rational
 step-by-step reasoning and once in a model of reinforcement learning. We give sufficient conditions for equivalence of bidirectional
 optimality and the former, and show based on numerical simulations that bidirectional optimization may be thought of as a
 process of reinforcement learning with lateral inhibition.
 
 
	

  We introduce a substructural propositional calculus of Sequential Dynamic Logic that subsumes a propositional part of dynamic
 predicate logic, and is shown to be expressively equivalent to propositional dynamic logic. Completeness of the calculus with
 respect to the intended relational semantics is established.
 
 
	

  In this paper we are going to show that error coping strategies play an essential role in linguistic pragmatics. We study
 the effect of noisy speaker strategies within a framework of signalling games with feedback loop. We distinguish between cases in which errors
 occur in message selection and cases in which they occur in signal selection. The first type of errors affects the content
 of an utterance, and the second type its linguistic expression. The general communication model is inspired by the Shannon“Weaver
 communication model. We test the model by a number of benchmark examples, including examples of relevance implicatures, quantity
 implicatures, and presupposition accommodation.
 
 
	

  Indefinites face competition at two levels: Presupposition and content. The antipresupposition hypothesis predicts that they
 signal the opposite of familiarity, or uniqueness, namely, novelty, or non-uniqueness. At the level of descriptive content,
 they are pressured from two sides: definites expressing identity and another phrases expressing difference, and Gricean reasoning predicts that indefinites signal both difference and identity and are
 infelicitous when definites and another phrases are felicitous. However, occasionally a space opens between the and another, for a to fill. This is in part due to conditions handicapping the or another semantically, in part to another's phonological handicap. The division of labor between determiners in the field of difference and sameness is thus the result
 of an intricate competition. We model this competition in a version of game-theoretic pragmatics.
 
 
	

  Dutch allows for variation as to whether the first position in the sentence is occupied by the subject or by some other constituent,
 such as the direct object. In particular situations, however, this commonly observed variation in word order is ˜frozen' and
 only the subject appears in first position. We hypothesize that this partial freezing of word order in Dutch can be explained
 from the dependence of the speaker's choice of word order on the hearer's interpretation of this word order. A formal model
 of this interaction between the speaker's perspective and the hearer's perspective is presented in terms of bidirectional
 Optimality Theory. Empirical predictions of this model regarding the interaction between word order and definiteness are confirmed
 by a quantitative corpus study.
 
 
	

  Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on
 qualitative comparisons of information added. Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct,
 incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information
 added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional
 probability. We look at two ways to obtain a quantitative conception of information added. One, the most direct, mirrors Bernard
 Koopman's construction of conditional probability: by making a strong structural assumption, it leads to a measure that is,
 transparently, some function of a function P which is, formally, an assignment of conditional probability (in fact, a Popper function). P reverses the information added order and mislocates the natural zero of the scale so some transformation of this scale is
 needed but the derivation of P falls out so readily that no particular transformation suggests itself. The Cox“Good“Aczél method assumes the existence of
 a quantitative measure matching the qualitative relation, and builds on the structural constraints to obtain a measure of
 information that can be rescaled as, formally, an assignment of conditional probability. A classical result of Cantor's, subsequently
 strengthened by Debreu, goes some way towards justifying the assumption of the existence of a quantitative scale. What the
 two approaches give us is a pointer towards a novel interpretation of probability as a rescaling of a measure of information
 added.
 
 
	

  A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version
 of this principle is then derived.