In this section we describe a logical framework that offers the resources for properly representing what is right about the reversibility objection without leading to inconsistency. In the first case, extensional synonymy is being considered, for example, a. Belnap department of philosophy, university of pittsburgh, 1001 cathedral of learning, pittsburgh, pa 15260, usa this paper follows part i of our essay on case intensional first order logic cifol. In the rst of these they do an especially nice job of explaining the virtues of ml, and their own caseintensional first order logic cifol, in. But first we need to sketch the alternative framework. Tutorial on truth values fabien schang and heinrich wansing lectures 1 and 2, references heinrich wansing. Inference in firstorder logic department of computer. Classical firstorder logic can be extended in two different ways to serve. The complexity of the dependence operator pdf paperity. Deduction rules for caseintensional higherorder logic. Caseintensional first order logic by nuel belnap and thomas muller download pdf 702 kb.
To the memory of arthur prior formal properties of now. The perfect being argument in caseintensional logic matthew dickau 1 of 9 the perfect being argument in caseintensional logic the perfect being argument for gods existence is the following deduction. This paper follows part i of our essay on caseintensional first order logic cifol. Our system bhcifol adds structure to the cases, which in part i formed just. This is part i of a twopart essay introducing caseintensional first order logic cifol, an easytouse, uniform, powerful, and useful combination of firstorder logic with modal logic resulting from philosophical and technical modifications of bressans general interpreted modal calculus yale university press 1972. The term temporal logic has been broadly used to cover all approaches to reasoning about time and temporal information, as well as their formal representation, within a logical framework, and also more narrowly to refer specifically to the modal logic type of approach introduced around 1960 by arthur prior under the name tense logic and subsequently developed further by many logicians and. Solving the caesar problem without categorical sortals solving the caesar problem without categorical sortals. Nuel belnap on indeterminism and free action uni konstanz. We show that in that framework we can account for the role of sortals in. If a property is positive, its negation is not positive. The reversibility objection against the second law of thermodynamics viewed, and avoided, from a logical point of view. Caseintensional first order logic ii branching histories. To submit an update or takedown request for this paper, please submit an updatecorrectionremoval request.
We define an observation network as a network of agents who each have a vocabulary, a knowledge base in firstorder logic, and a set of potential observations. Journal of philosophical logic, volume 43, issue 5 springer. Our system bhcifol adds structure to the cases, which in part i formed just a set. For the case of arrows theorem, which does not apply in the case. In this introduction to the outstanding contributions to logic volume devoted to nuel belnaps work on indeterminism and free action, we provide a brief overview of some of the formal frameworks and methods involved in belnaps work on these topics. Bressan based his calculus on carnaps method of extension and intension. David toman and damian niwinski, firstorder queries over temporal databases inexpressible in temporal logic, advances in database technology edbt 96, 10. The volume also contains an extended biographical interview. Deduction rules for caseintensional higherorder logic matthew dickau 4 of 11 the brackets in these expressions are optional. An unusual feature of this algorithm is the use of the inclusionexclusion principle more precisely, of the mobiusinversionformula, which allows for distinct. This is part i of a twopart essay introducing caseintensional firstorder logic cifol, an easytouse, uniform, powerful, and useful combination of first order logic with modal logic resulting from philosophical and technical modifications of bressans general interpreted modal calculus yale university press 1972. Relevant alternatives and subjunctivism epistemic closure and epistemic logic i. This paper follows part i of our essay on caseintensional firstorder logic cifol.
We illustrate the importance of tracing via a discussion of possible experiments in science and in everyday life. The journal of philosophical logic provides a forum for work at the crossroads of philosophy and logic, old and new, with contributions ranging from conceptual to technical. Alscher arithmetization of geometry as interpretation between firstorder theories break. Universal logic iii estoril 2010 tutorial on truth values. Firstorder logic propositional logic only deals with facts, statements that may or may not be true of the world, e. Nuel belnap on indeterminism and free action thomas. Caseintensional first order logic i toward a theory. This is part i of a twopart essay introducing caseintensional first order logic cifol, an easytouse, uniform, powerful, and useful. Full text of nuel belnap on indeterminism and free action electronic resource see other formats. We present cifol, an 1 easytouse, 2 uniform, 3 powerful, and 4 useful combination of first order logic with modal logic resulting from philosophical and technical modifications of bressan 1972. The perfect being argument in caseintensional logic. But that means todays subject matter is firstorder logic, which is extending propositional logic so that we can talk about things.
In cifol, truth is relative to cases, where cases play the formal role of worlds but with. Apr 21, 2014 we illustrate the importance of tracing via a discussion of possible experiments in science and in everyday life. Here we refine and enrich cifol to take account of indeterminism, relying for that purpose on a branching structure that we call branching histories. Belnap department of philosophy, university of pittsburgh, 1001 cathedral of learning, pittsburgh, pa 15260, usa this paper follows part i of our essay on caseintensional firstorder logic cifol. The volume also contains an extended biographical interview with nuel belnap.
The journal places a special emphasis on the applications of philosophical logic in other disciplines, not only in mathematics and the natural sciences but also, for example, in computer science, artificial intelligence, cognitive science, linguistics, jurisprudence, and the social sciences, such as economics, sociology, and political science. Synonymy a binary relation between two equivalent but not identical expressions. Employing a local notion of modal consistency in branching theories. Caseintensional logic as a framework for tracing things from case to case. This is part i of a twopart essay introducing case intensional first order logic cifol, an easytouse, uniform, powerful, and useful combination of first order logic with modal logic resulting from philosophical and technical modifications of bressans general interpreted modal calculus yale university press 1972. Accordingly, the journal invites papers in all of the traditional areas of philosophical logic, including but not limited to. The term temporal logic has been broadly used to cover all approaches to reasoning about time and temporal information, as well as their formal representation, within a logical framework, and also more narrowly to refer specifically to the modallogic type of approach introduced around 1960 by arthur prior under the name tense logic and subsequently developed further by many. Full text of nuel belnap on indeterminism and free action. We introduce a framework of branching histories to. Aug 25, 20 this paper follows part i of our essay on caseintensional firstorder logic cifol. From highest priority to lowest, the order of operations for the truthfunctional connectives is. Nuel belnap on indeterminism and free action som ebog.
Firstorder logic formalisation of impossibility theorems in. This dissertation provides a new semantics for first order modal logic. Agents can make inferences and report them to other agents to whom they are linked, but communication is restricted to the common vocabulary of the reporter and recipient. In this paper we offer a formallogical analysis of the famous reversibility objection against the second law of thermodynamics. The logical problem of the trinity and the strong theory of relative identity the logical problem of the trinity and the. This volume seeks to further the use of formal methods in clarifying one of the central problems of. This dissertation provides a new semantics for firstorder modal logic. The reader is asked to make the following changes in the enumeration of the axioms and theorems. In part i we introduced cifol, a caseintensional firstorder logic, as a general purpose quantified modal logic derived from bressan. In cifol, truth is relative to cases, where cases play the formal role of worlds but with less pretension. Nuel belnap on indeterminism and free action electronic. The reversibility objection against the second law of.
Caseintensional first order logic i toward a theory of sorts nuel belnap thomas muller. Synonymy article about synonymy by the free dictionary. After pointing out shortcomings of standard systems of quantified modal logic, we introduce cifol, case intensional first order logic, as a newly established formal framework that helps to elucidate the notion of tracing. It also introduces caseintensional first order logic cifol, a general intensional logic offering resources for a firstorder extension of the mentioned frameworks and a recent research focus of belnaps. The identity of individuals in a strict functional calculus. The identity of individuals in a strict functional. In caseintensional first oder logic, which derives from bressans work, a predication. Such an intensional first order logic, or quantified modal logic. We reconstruct the objection as a deductive argument leading to a contradiction, employing resources of standard quantified modal logic and thereby highlighting explicit and implicit assumptions with respect to possibility, identity, and their interaction. Stepanov propositional logic of reflexive sentences or truth without contradiction d. I toward a theory of sorts article pdf available in journal of philosophical logic 4323 june 20 with 80 reads.
This is part i of a twopart essay introducing caseintensional first order logic cifol, an easytouse, uniform, powerful, and useful combination of firstorder. Substance and firstorder quantification over individual. We introduce a framework of branching histories to take account of indeterminism. This paper follows part i of our essay on caseintensional. Cifol is a recent research focus of belnaps, as reflected in his own contribution to this volume. Case 2 uses the extensionof operator, converting a term of intensional. We start with the flexible notion of possible cases rather than possible worlds, and we apply carnaps method of extension and intension for terms and sentences uniformly, to arrive at the system of caseintensional first order logic, cifol. It is philosophicallymotivated by the epistemic reading of modal operators and, in particular, three desiderata in the analysis of epistemic modalities. Mar 22, 2014 cifol is defined in belnap and muller 20 j phil logic 20 as the firstorder fragment of aldo bressans higherorder modal typed calculus \mc u \.
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