Stit logic of justification announcements: a completeness result

2018 ◽  
Vol 28 (6) ◽  
pp. 1031-1064 ◽  
Author(s):  
Grigory K Olkhovikov
Keyword(s):  
Stit Logic ◽  
Completeness Result

scholarly journals Justification announcements in discrete time. Part II: Frame definability results

2018 ◽  
Vol 27 (5) ◽  
pp. 671-692
Author(s):  
Grigory K Olkhovikov
Keyword(s):  
Discrete Time ◽  
Time Structure ◽  
Stit Logic ◽  
Completeness Result ◽  
Time Part

Abstract In Part I of this paper we presented a Hilbert-style system $\Sigma _D$ axiomatizing stit logic of justification announcements interpreted over models with discrete time structure. In this part, we prove three frame definability results for $\Sigma _D$ using three different definitions of a frame plus another version of completeness result.

scholarly journals Choice-Driven Counterfactuals

2021 ◽  
Author(s):  
Ilaria Canavotto ◽  
Eric Pacuit
Keyword(s):  
Choice Behavior ◽  
The Other ◽  
Philosophical Literature ◽  
Stit Logic

AbstractIn this paper, we investigate the semantics and logic of choice-driven counterfactuals, that is, of counterfactuals whose evaluation relies on auxiliary premises about how agents are expected to act, i.e., about their default choice behavior. To do this, we merge one of the most prominent logics of agency in the philosophical literature, namely stit logic (Belnap et al. 2001; Horty 2001), with the well-known logic of counterfactuals due to Stalnaker (1968) and Lewis (1973). A key component of our semantics for counterfactuals is to distinguish between deviant and non-deviant actions at a moment, where an action available to an agent at a moment is deviant when its performance does not agree with the agent’s default choice behavior at that moment. After developing and axiomatizing a stit logic with action types, instants, and deviant actions, we study the philosophical implications and logical properties of two candidate semantics for choice-driven counterfactuals, one called rewind models inspired by Lewis (Nous13(4), 455–476 1979) and the other called independence models motivated by well-known counterexamples to Lewis’s proposal Slote (Philos. Rev.87(1), 3–27 1978). In the last part of the paper we consider how to evaluate choice-driven counterfactuals at moments arrived at by some agents performing a deviant action.

Completeness of category-based equational deduction

1995 ◽  
Vol 5 (1) ◽  
pp. 9-40 ◽  
Author(s):  
Răzvan Diaconescu
Keyword(s):  
Logic Programming ◽  
Model Theory ◽  
Constraint Logic Programming ◽  
Horn Clause ◽  
Abstract Model ◽  
Abstract Model Theory ◽  
Completeness Result ◽  
Semantic Treatment ◽  
Theory Framework ◽  
Deduction Modulo

Equational deduction is generalised within a category-based abstract model theory framework, and proved complete under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and valuations as model morphisms rather than functions. Applications include many- and order-sorted (conditional) equational logics, Horn clause logic, equational deduction modulo a theory, constraint logics, and more, as well as any possible combination among them. In the cases of equational deduction modulo a theory and of constraint logic the completeness result is new. One important consequence is an abstract version of Herbrand's Theorem, which provides an abstract model theoretic foundation for equational and constraint logic programming.

A General Completeness Result in Refinement

2000 ◽  
pp. 201-218 ◽  
Author(s):  
Yoshiki Kinoshita ◽  
John Power
Keyword(s):  
Completeness Result

scholarly journals Internal coalgebras in cocomplete categories: Generalizing the Eilenberg–Watts theorem

2020 ◽  
pp. 2150165 ◽  
Author(s):  
Laurent Poinsot ◽  
Hans E. Porst
Keyword(s):  
Left Adjoint ◽  
Adjoint Functors ◽  
Locally Presentable Category ◽  
Completeness Result ◽  
Lawvere Theory

The category of internal coalgebras in a cocomplete category [Formula: see text] with respect to a variety [Formula: see text] is equivalent to the category of left adjoint functors from [Formula: see text] to [Formula: see text]. This can be seen best when considering such coalgebras as finite coproduct preserving functors from [Formula: see text], the dual of the Lawvere theory of [Formula: see text], into [Formula: see text]: coalgebras are restrictions of left adjoints and any such left adjoint is the left Kan extension of a coalgebra along the embedding of [Formula: see text] into [Formula: see text]. Since [Formula: see text]-coalgebras in the variety [Formula: see text] for rings [Formula: see text] and [Formula: see text] are nothing but left [Formula: see text]-, right [Formula: see text]-bimodules, the equivalence above generalizes the Eilenberg–Watts theorem and all its previous generalizations. By generalizing and strengthening Bergman’s completeness result for categories of internal coalgebras in varieties, we also prove that the category of coalgebras in a locally presentable category [Formula: see text] is locally presentable and comonadic over [Formula: see text] and, hence, complete in particular. We show, moreover, that Freyd’s canonical constructions of internal coalgebras in a variety define left adjoint functors. Special instances of the respective right adjoints appear in various algebraic contexts and, in the case where [Formula: see text] is a commutative variety, are coreflectors from the category [Formula: see text] into [Formula: see text].

A simple proof of a completeness result for leads-to, in the UNITY logic

1992 ◽  
Vol 44 (3) ◽  
pp. 171
Author(s):  
Jan Pachl
Keyword(s):  
Simple Proof ◽  
Completeness Result

Deducing fairness properties in UNITY logic—a new completeness result

1995 ◽  
Vol 17 (1) ◽  
pp. 16-27 ◽  
Author(s):  
Yih-Kuen Tsay ◽  
Rajive L. Bagrodia
Keyword(s):  
Completeness Result

scholarly journals Deontic epistemic stit logic distinguishing modes of mens rea

2011 ◽  
Vol 9 (2) ◽  
pp. 137-152 ◽  
Author(s):  
Jan Broersen
Keyword(s):  
Mens Rea ◽  
Stit Logic

CONTEXTUAL LOGIC WITH MODALITIES FOR TIME AND SPACE

2008 ◽  
Vol 1 (4) ◽  
pp. 433-458 ◽  
Author(s):  
HAIM GAIFMAN
Keyword(s):  
Natural Language ◽  
Deductive System ◽  
Context Dependence ◽  
Full Detail ◽  
Philosophical Discussion ◽  
Modal Operators ◽  
Completeness Result ◽  
Temporal And Spatial ◽  
Linguistic Usage ◽  
Temporal Modality

We develop a formal apparatus to be used as a tool in analyzing common kinds of context dependence in natural language, and their interaction with temporal and spatial modalities. It is based on context-operators, which act on wffs. The interplay between the various modalities and the context-operators is one of the main targets of the analysis. Statements made by different people at different times in different places, using the same personal temporal and spatial indexicals, can be represented in the system, and can be combined by sentential connectives and be subject to quantification. The use of spatial modality and the suggested treatment of adverbial phrases are new as far as we know. So is a certain variant of temporal modality. In the nontechnical part, consisting of Sections 1 and 2, we discuss the role that formalisms can, in principle, play in the analysis of linguistic usage; this is followed by a philosophical discussion of various kinds of context dependence. The semitechnical part, Section 3, introduces the system's components, the context, and the modal operators, and explains their use via natural language examples. In Section 4 the formal language and its semantics are defined, in full detail. The temporal and spatial sublanguages constitute separate sorts, which interact through the modal operators and the context-operators. A sound deductive system is given and a completeness result is stated, without proof.

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