Coalescing: Syntactic Abstraction for Reasoning in First-Order Modal Logics

Doligez, Damien; Kriener, Jael; Lamport, Leslie; Libal, Tomer; Merz, Stephan

doi:10.29007/cpbz

Cited by 3 publications

(3 citation statements)

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“…For instance, it seems interesting to consider the application of Checkers to objects composed from proofs coming from different proof calculi. One example of such objects are coalesced proofs, described in [Doligez et al 2014]. In this work, a proof evidence is created by using modal theorem provers alongside first-order ones.…”

Section: Discussionmentioning

confidence: 99%

A general proof certification framework for modal logic

Libal¹,

Volpe²

2019

Math. Struct. Comp. Sci.

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One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the usage of a common specification language and of a small and trusted kernel in order to check proofs coming from different sources and for different logics. By relying on that idea and by using a classical focused sequent calculus as a kernel, we propose here a general framework for checking modal proofs. We present the implementation of the framework in a Prolog-like language and show how it is possible to specialize it in a simple and modular way in order to cover different proof formalisms, such as labeled systems, tableaux, sequent calculi and nested sequent calculi. We illustrate the method for the logic K by providing several examples and discuss how to further extend the approach. † When calculating the size of the program, we placed each atomic predicate on a new line. ‡ In fact, it is possible to show that every modal formula can be translated into a formula in the fragment of first-order logic which uses only two variables [Blackburn and Van Benthem 2007]. By the decidability of such a fragment, an easy proof of the decidability of the modal logic K follows.

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Section: Discussionmentioning

confidence: 99%

A general proof certification framework for modal logic

Libal¹,

Volpe²

2019

Math. Struct. Comp. Sci.

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“…Similarly, in a temporal step (such as the QED step above), any first-order formulas are abstracted by propositional variables. This transformation is called coalescing [20]; it is necessary so that back-end provers see the proof obligation either as . .…”

Section: The Tla + Proof Systemmentioning

confidence: 99%

Formal specification and verification

Merz¹

2019

Concurrency: The Works of Leslie Lamport

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“…Mostly psychological experiments investigated reasoning of inference about what is the case [ 21 – 23 ], students were asked inference validity, evaluation task (ET) or production task (PT) and problem-based on negations, connectives, if, and, or syllogism. There are very few findings of modal logic reasoning [ 24 , 25 ] cover these all work in one experimental study.…”

Section: Introductionmentioning

confidence: 99%

An experimental study of classical truth logic on multi-propositions consistent and incompatible: Dual-process theories and modal syllogistic of deduction

Waheed,

Habib

2024

PLoS ONE

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This study looked at a classical truth logic of multi-propositions that is new in some ways: [1] Alethic modalities were mixed with logical consistency and incompatibility in a single plate form, i.e., necessary consistency (NC), possible consistency (PC)/ possible incompatibility (PI) and impossible incompatibility (IPI); [2] multi-propositions were judged by individuals as either NC, PC/PI, or IPI; [3] Four quantifiers; All (∀), No (∼∀), Some (∃), and Some Not (∼∃) of four propositional modes and three shapes (, ▱ and ) are used to evaluate predictions; and [4] it inspired by multi-propositional of dual-process theories (DPTs) of deduction and modal syllogistic of multi-propositions, from which logicians have derived general hypotheses. HP 1- Individuals will more likely to endorse inferences as PC/PI rather than NC. HP 2: It’s easier to calculate that inference has PC/ PI if it has also NC. Generally, logicians predict more endorsing PC for NC than for PI proposition. HP 3: It’s easier to calculate that inference is not NC if it is also not PC. Generally, logicians predict more PI than IPI proposition endorses as NC. A modal syllogistic as a classical truth logic is presented by multi-propositions (two premises and one inference), each one from four modes has quantifiers such as universal quantifiers and existential quantifier; ∀, ∼∀, ∃, and ∼ ∃. They were evaluated by a single-mental model (Experiment I) and a multi-mental model (Experiment II). Logicians applied the immediate inference task (IIT), evaluation task (ET), and production task (PT) to evaluate three experiments. The results of the experiments suggested that students mostly endorsed PC/PI inferences over NC inferences. Even when logicians divided PC/PI separately as PC and PI, individuals endorsed PC most likely as compared to NC, and PI than IPI. Logicians also highlighted fallacies that were continuously resisted and endorsed when students were asked to judge multi-propositions that had NC. The purpose of this experimental study is to present a glimpse of students’ endorsement of multi-propositions and explain that each individual has a different working memory and intelligence.

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Coalescing: Syntactic Abstraction for Reasoning in First-Order Modal Logics

Abstract: We present a syntactic abstraction method to reason about first-order modal logics by using theorem provers for standard first-order logic and for propositional modal logic.

Cited by 3 publications

References 8 publications

A general proof certification framework for modal logic

A general proof certification framework for modal logic

Formal specification and verification

An experimental study of classical truth logic on multi-propositions consistent and incompatible: Dual-process theories and modal syllogistic of deduction

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