19 Applications of modal logic in linguistics

Moss, Lawrence S.; Tiede, Hans-Jörg

doi:10.1016/s1570-2464(07)80022-x

Cited by 6 publications

(5 citation statements)

References 56 publications

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“…For readers who prefer modal logic to fragments of second-order logic, the following reformulation may seem more attractive: The temporal logic of strings captures star-free languages and propositional dynamic logic captures regular languages (see e.g. Moss and Tiede, 2006).…”

Section: Semantic Processingmentioning

confidence: 99%

Tractability and the computational mind

Szymanik¹,

Verbrugge

2018

The Routledge Handbook of the Computational Mind

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Section: Semantic Processingmentioning

confidence: 99%

Tractability and the computational mind

Szymanik¹,

Verbrugge

2018

The Routledge Handbook of the Computational Mind

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“…Modal logics have been extensively studied in the context of knowledge representation and reasoning and, more broadly, artificial intelligence, providing the ability to qualify truth according to different modalities, most commonly the alethic modalities of necessity and possibility. Several practical applications of modal logics have been proposed, such as analysing syntax structures and natural language semantics in linguistics (Moss and Tiede 2007), belief and trust in multi-agent systems (Liau 2003) and weak models of distributed computing (Hella et al . 2015).…”

Section: Introductionmentioning

confidence: 99%

Modal Logic S5 Satisfiability in Answer Set Programming

Alviano¹,

Batsakis²,

Baryannis³

2021

Theory and Practice of Logic Programming

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Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5 formulas commonly rely on Skolemisation to convert them into propositional logic formulas, essentially by introducing copies of propositional atoms for each set of interpretations (possible worlds). This approach is simple, but often results into large formulas that are too difficult to process, and therefore more parsimonious constructions are required. In this work, we propose to use Answer Set Programming for implementing such constructions, and in particular for identifying the propositional atoms that are relevant in every world by means of a reachability relation. The proposed encodings are designed to take advantage of other properties such as entailment relations of subformulas rooted by modal operators. An empirical assessment of the proposed encodings shows that the reachability relation is very effective and leads to comparable performance to a state-of-the-art S5 solver based on SAT, while entailment relations are possibly too expensive to reason about and may result in overhead.

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“…The S5 logic [1] is another example, distinguishing essential truth (true in all worlds) and possible truth (true only in some worlds). Modal logics have many applications in numerous domains, including verification of concurrent systems [2], reasoning about computer programs [3], artificial intelligence [4], robotics [5], linguistics [6], and philosophy [7]. This is a strong indication of how complex real-life problems are, and that new logical formalisms are continuously being introduced to address them effectively.…”

Section: Introductionmentioning

confidence: 99%

Towards Modal Software Engineering

Shahin

2021

2021 IEEE/ACM 43rd International Conference on Software Engineering: New Ideas and Emerging Results (ICSE-NIER)

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In this paper we introduce the notion of Modal Software Engineering: automatically turning sequential, deterministic programs into semantically equivalent programs efficiently operating on inputs coming from multiple overlapping worlds. We are drawing an analogy between modal logics, and software application domains where multiple sets of inputs (multiple worlds) need to be processed efficiently. Typically those sets highly overlap, so processing them independently would involve a lot of redundancy, resulting in lower performance, and in many cases intractability. Three application domains are presented: reasoning about feature-based variability of Software Product Lines (SPLs), probabilistic programming, and approximate programming.

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19 Applications of modal logic in linguistics

Cited by 6 publications

References 56 publications

Tractability and the computational mind

Tractability and the computational mind

Modal Logic S5 Satisfiability in Answer Set Programming

Towards Modal Software Engineering

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