Update rules and semantic universals

Incurvati, Luca; Sbardolini, Giorgio

doi:10.1007/s10988-022-09362-1

Cited by 5 publications

(15 citation statements)

References 45 publications

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“…The explanation developed in this paper has to do with structural (logical) constraints on informationtransmission in a conversational setting. 1 Following [14], a bilateral system of updates is dened in which ∧, ∨, and nor, can be straightforwardly expressed, but that lacks nand and all other connectives. Accordingly, semantic universals may depend on cognitive asymmetries in the dynamic processing of logically structured information.…”

Section: Semantic Universalsmentioning

confidence: 99%

“…Following [14], two update systems are dened below. The rst, system U, encodes ∧, ∨, nor, but no other truth-function.…”

Section: Outline Of the Storymentioning

confidence: 99%

“…The denition of update by conjunction as sequence of updates is due to Irene Heim [11]. Update by disjunction reduces to Veltman's update rule for disjunction for the "negation-free" fragment of the language and in H [23] (see [14]).…”

Section: System Umentioning

confidence: 99%

“…It can also be shown that the monotonicity properties for ∧, ∨, and nor follow from the properties of the update system[14]. Thus the important observation that natural language lexical operators are monotone follows from the logic of speech acts[3] 6.…”

mentioning

confidence: 97%

“…A competing hypothesis is based on the possibility of expressing missing operators by means of scalar reasoning[6,12,15,22]. For a criticism of this approach, see[14].…”

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confidence: 99%

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Assertion, Rejection, and Semantic Universals

Sbardolini

2021

Logic, Rationality, and Interaction

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Natural language contains simple lexical items for some but not all Boolean operators. English, for example, contains conjunction and, disjunction or, negated disjunction nor, but no word to express negated conjunction *nand nor any other Boolean connective. Natural language grammar can be described by a logic that expresses what the lexicon can express by its primitives, and the rest compositionally. Such logic for propositional connectives is described here as a bilateral extension of update semantics. The basic intuition is that a context can be updated by assertion or by rejection, and by one or multiple propositions at once. These distinctions suce to characterize the logic of the lexicon.

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Section: Semantic Universalsmentioning

confidence: 99%

“…Following [14], two update systems are dened below. The rst, system U, encodes ∧, ∨, nor, but no other truth-function.…”

Section: Outline Of the Storymentioning

confidence: 99%

Section: System Umentioning

confidence: 99%

mentioning

confidence: 97%

“…A competing hypothesis is based on the possibility of expressing missing operators by means of scalar reasoning[6,12,15,22]. For a criticism of this approach, see[14].…”

mentioning

confidence: 99%

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Assertion, Rejection, and Semantic Universals

Sbardolini

2021

Logic, Rationality, and Interaction

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The Logic of Lexical Connectives

Sbardolini¹

2023

J Philos Logic

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Natural language does not express all connectives definable in classical logic as simple lexical items. Coordination in English is expressed by conjunction and, disjunction or, and negated disjunction nor. Other languages pattern similarly. Non-lexicalized connectives are typically expressed compositionally: in English, negated conjunction is typically expressed by combining negation and conjunction (not both). This is surprising: if $$\wedge $$ ∧ and $$\vee $$ ∨ are duals, and the negation of the latter can be expressed lexically (nor), why not the negation of the former? I present a two-tiered model of the semantics of the binary connectives. The first tier captures the expressive power of the lexicon: it is a bilateral state-based semantics that, under a restriction, can express all and only the distinctions that can be expressed by the lexicon of natural language (and, or, nor). This first tier is characterized by rejection as non-assertion and a Neglect Zero assumption. The second tier is obtained by dropping the Neglect Zero assumption and enforcing a stronger notion of rejection, thereby recovering classical logic and thus definitions for all Boolean connectives. On the two-tiered model, we distinguish the limited expressive resources of the lexicon and the greater combinatorial expressive power of the language as a whole. This gives us a logic-based account of compositionality for the Boolean fragment of the language.

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Recursive Numeral Systems Optimize the Trade‐off Between Lexicon Size and Average Morphosyntactic Complexity

Denić,

Szymanik

2024

Cognitive Science

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Human languages vary in terms of which meanings they lexicalize, but this variation is constrained. It has been argued that languages are under two competing pressures: the pressure to be simple (e.g., to have a small lexicon) and to allow for informative (i.e., precise) communication, and that which meanings get lexicalized may be explained by languages finding a good way to trade off between these two pressures. However, in certain semantic domains, languages can reach very high levels of informativeness even if they lexicalize very few meanings in that domain. This is due to productive morphosyntax and compositional semantics, which may allow for construction of meanings which are not lexicalized. Consider the semantic domain of natural numbers: many languages lexicalize few natural number meanings as monomorphemic expressions, but can precisely convey very many natural number meanings using morphosyntactically complex numerals. In such semantic domains, lexicon size is not in direct competition with informativeness. What explains which meanings are lexicalized in such semantic domains? We will propose that in such cases, languages need to solve a different kind of trade‐off problem: the trade‐off between the pressure to lexicalize as few meanings as possible (i.e, to minimize lexicon size) and the pressure to produce as morphosyntactically simple utterances as possible (i.e, to minimize average morphosyntactic complexity of utterances). To support this claim, we will present a case study of 128 natural languages' numeral systems, and show computationally that they achieve a near‐optimal trade‐off between lexicon size and average morphosyntactic complexity of numerals. This study in conjunction with previous work on communicative efficiency suggests that languages' lexicons are shaped by a trade‐off between not two but three pressures: be simple, be informative, and minimize average morphosyntactic complexity of utterances.

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Update rules and semantic universals

Cited by 5 publications

References 45 publications

Assertion, Rejection, and Semantic Universals

Assertion, Rejection, and Semantic Universals

The Logic of Lexical Connectives

Recursive Numeral Systems Optimize the Trade‐off Between Lexicon Size and Average Morphosyntactic Complexity

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