180 research outputs found
Decidability of quantified propositional intuitionistic logic and S4 on trees
Quantified propositional intuitionistic logic is obtained from propositional
intuitionistic logic by adding quantifiers \forall p, \exists p over
propositions. In the context of Kripke semantics, a proposition is a subset of
the worlds in a model structure which is upward closed. Kremer (1997) has shown
that the quantified propositional intuitionistic logic H\pi+ based on the class
of all partial orders is recursively isomorphic to full second-order logic. He
raised the question of whether the logic resulting from restriction to trees is
axiomatizable. It is shown that it is, in fact, decidable. The methods used can
also be used to establish the decidability of modal S4 with propositional
quantification on similar types of Kripke structures.Comment: v2, 9 pages, corrections and additions; v1 8 page
Deciding logics of linear Kripke frames with scattered end pieces
We show that logics based on linear Kripke frames – with or without constant domains – that have a scattered end piece are not recursively enumerable.This is done by reduction to validity in all finite classical models
Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents
This paper employs the linear nested sequent framework to design a new
cut-free calculus LNIF for intuitionistic fuzzy logic--the first-order G\"odel
logic characterized by linear relational frames with constant domains. Linear
nested sequents--which are nested sequents restricted to linear
structures--prove to be a well-suited proof-theoretic formalism for
intuitionistic fuzzy logic. We show that the calculus LNIF possesses highly
desirable proof-theoretic properties such as invertibility of all rules,
admissibility of structural rules, and syntactic cut-elimination.Comment: Appended version of the paper "Syntactic Cut-Elimination for
Intuitionistic Fuzzy Logic via Linear Nested Sequents", accepted to the
International Symposium on Logical Foundations of Computer Science (LFCS
2020
The Epsilon Calculus and Herbrand Complexity
Hilbert's epsilon-calculus is based on an extension of the language of
predicate logic by a term-forming operator . Two fundamental
results about the epsilon-calculus, the first and second epsilon theorem, play
a role similar to that which the cut-elimination theorem plays in sequent
calculus. In particular, Herbrand's Theorem is a consequence of the epsilon
theorems. The paper investigates the epsilon theorems and the complexity of the
elimination procedure underlying their proof, as well as the length of Herbrand
disjunctions of existential theorems obtained by this elimination procedure.Comment: 23 p
Completeness and Decidability Results for First-order Clauses with Indices
Session: Inference systems (www.cl.cam.ac.uk/~gp351/cade24)International audienceWe define a proof procedure that allows for a limited form of inductive reasoning. The first argument of a function symbol is allowed to belong to an inductive type. We will call such an argument an index. We enhance the standard superposition calculus with a loop detection rule, in order to encode a particular form of mathematical induction. The satisfiability problem is not semi-decidable, but some classes of clause sets are identified for which the proposed procedure is complete and/or terminating
Military business and the business of the military
Contrary to dominant approaches that locate the causes for military entrepreneurialism in eastern Democratic Republic of the Congo predominantly in criminal military elites, this article highlights the importance of the Congolese military’s (FARDC) civilian context for understanding military revenue-generation. It analyses how the latter is shaped by structures of domination, signification and legitimisation that drive and are driven by the FARDC’s governance, private protection and security practices. It argues that these practices contribute to bestowing a degree of legitimacy on both the FARDC’s position of power and some of its revenue-generation activities. Furthermore, by emphasising that the FARDC’s regulatory and protection practices are partly the product of popular demands and the routine actions of civilians, the article contends that the causes of military revenue-generation are co-located in the military’s civilian environment. In this manner, it offers a more nuanced conceptualisation of military entrepreneurialism, thus opening up new perspectives on policy interventions in this area
Bounding Resource Consumption with Gödel-Dummett Logics
International audienceGödel-Dummett logic LC and its finite approximations LCn are the intermediate logics complete w.r.t. linearly ordered Kripke models. In this paper, we use LCn logics as a tool to bound resource consumption in some process calculi. We introduce a non-deterministic process calculus where the consumption of a particular resource denoted * is explicit and provide an operational semantics which measures the consumption of this resource.We present a linear transformation of a process P into a formula f of LC. We show that the consumption of the resource by P can be bounded by the positive integer n if and only if the formula f admits a counter-model in LCn. Combining this result with our previous results on proof and counter-model construction for LCn, we conclude that bounding resource consumption is (linearly) equivalent to searching counter-models in LCn
The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łukasiewicz’s 3-Valued Logic Ł3
25 p.We consider the logics determined by the set of all natural implicative expansions of Kleene’s strong 3-valued matrix (with both only one and two designated values) and select the class of all logics functionally equivalent to Łukasiewicz’s 3-valued logic Ł3. The concept of a “natural implicative matrix” is based upon the notion of a “natural conditional” defined in Tomova (Rep Math Log 47:173–182, 2012).S
A Gendered Imperative: Does Sexual Violence Attract UN Attention in Civil Wars?
There is increasing awareness that sexual violence is distinct from other aspects of civilian victimization in civil wars. Few studies have examined the independent impact of such violence on responses to civil wars as compared to “traditional” forms of violence. This paper explores whether reports of high levels of rape and sexual violence increase the probability of UN attention to conflicts and calls to action. In so doing, we combine original data on UN Security Council resolutions with data on sexual violence in armed conflict and estimate the impact of sexual violence on UN attention to all civil wars from 1990-2009. We show that the effects of sexual violence on the number and level of UNSC resolutions are shown to be significant even when controlling for other important determinants of UN action. These findings have important implications for understanding how the UN has expanded its view on protecting civilians
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