7,984 research outputs found
The Varieties of Ought-implies-Can and Deontic STIT Logic
STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a variety of alternative
OiC interpretations have been proposed and discussed. This paper provides a modular framework for deontic STIT that accounts for a multitude of OiC readings. In particular, we discuss, compare, and formalize ten such readings. We provide sound and complete sequent-style calculi for all of the various STIT logics accommodating these OiC principles. We formally analyze the resulting logics and discuss how the different OiC principles are logically related. In particular, we propose an endorsement principle describing which OiC readings logically commit one to other OiC readings
The Structure of Differential Invariants and Differential Cut Elimination
The biggest challenge in hybrid systems verification is the handling of
differential equations. Because computable closed-form solutions only exist for
very simple differential equations, proof certificates have been proposed for
more scalable verification. Search procedures for these proof certificates are
still rather ad-hoc, though, because the problem structure is only understood
poorly. We investigate differential invariants, which define an induction
principle for differential equations and which can be checked for invariance
along a differential equation just by using their differential structure,
without having to solve them. We study the structural properties of
differential invariants. To analyze trade-offs for proof search complexity, we
identify more than a dozen relations between several classes of differential
invariants and compare their deductive power. As our main results, we analyze
the deductive power of differential cuts and the deductive power of
differential invariants with auxiliary differential variables. We refute the
differential cut elimination hypothesis and show that, unlike standard cuts,
differential cuts are fundamental proof principles that strictly increase the
deductive power. We also prove that the deductive power increases further when
adding auxiliary differential variables to the dynamics
Failure of interpolation in the intuitionistic logic of constant domains
This paper shows that the interpolation theorem fails in the intuitionistic
logic of constant domains. This result refutes two previously published claims
that the interpolation property holds.Comment: 13 pages, 0 figures. Overlaps with arXiv 1202.1195 removed, the text
thouroughly reworked in terms of notation and style, historical notes as well
as some other minor details adde
Failure of interpolation in the intuitionistic logic of constant domains
This paper shows that the interpolation theorem fails in the intuitionistic
logic of constant domains. This result refutes two previously published claims
that the interpolation property holds.Comment: 13 pages, 0 figures. Overlaps with arXiv 1202.1195 removed, the text
thouroughly reworked in terms of notation and style, historical notes as well
as some other minor details adde
Classical System of Martin-Lof's Inductive Definitions is not Equivalent to Cyclic Proofs
A cyclic proof system, called CLKID-omega, gives us another way of
representing inductive definitions and efficient proof search. The 2005 paper
by Brotherston showed that the provability of CLKID-omega includes the
provability of LKID, first order classical logic with inductive definitions in
Martin-L\"of's style, and conjectured the equivalence. The equivalence has been
left an open question since 2011. This paper shows that CLKID-omega and LKID
are indeed not equivalent. This paper considers a statement called 2-Hydra in
these two systems with the first-order language formed by 0, the successor, the
natural number predicate, and a binary predicate symbol used to express
2-Hydra. This paper shows that the 2-Hydra statement is provable in
CLKID-omega, but the statement is not provable in LKID, by constructing some
Henkin model where the statement is false
Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General
This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment
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